Methods and Systems for Identifying and Deducing Multi-Element Fusion Propagation Nodes in Online Social Networks

Abstract

This invention provides a method and system for identifying and extrapolating multi-element fusion propagation nodes in online social networks, relating to the field of node data processing technology. The method includes: acquiring forwarding information of trending posts on social platforms, and constructing a forwarding network topology based on the forwarding information, where nodes in the network topology represent forwarding users and edges represent forwarding relationships between corresponding nodes; evaluating and ranking the importance of nodes in the forwarding network topology based on a centripetal centrality algorithm to obtain a node importance ranking; and dynamically simulating the information propagation process based on a strategy simulation algorithm according to the forwarding information of trending posts on social platforms, completing the propagation effect evaluation, and realizing the quantitative analysis of the propagation patterns of trending posts and the scientific evaluation of propagation effects. This provides data support and decision-making basis for propagation intervention, content guidance, and risk management on social platforms.

Description

Technical Field

[0001] This invention relates to the field of node data processing technology, and in particular to a method and system for identifying and deducing multi-element fusion propagation nodes in online social networks. Background Technology

[0002] With the rapid development of social networks and the continuous expansion of their user base, the timeliness and breadth of information dissemination have experienced explosive growth. "Trending posts" on certain hot topics spread widely across social media platforms in a very short time, exhibiting complex cross-sector and cross-regional dissemination chains. In this highly dynamic communication environment with a clear community structure, a few key dissemination nodes or influential figures often have a decisive impact on the speed of information dissemination, its coverage, and the direction of public opinion. They also serve as important bridging nodes connecting multiple groups. A lack of timely identification and intervention at these important dissemination nodes can lead to the rapid amplification of false information and the difficulty in controlling risky public opinion, ultimately negatively impacting social governance, corporate reputation, and public safety.

[0003] At the data level, social media platforms generally have interface quotas and speed limits, posing challenges to the acquisition, construction, and updating of data for large-scale trending posts and their dissemination networks. Meanwhile, some trending posts may be banned or deleted due to their sensitive topics or explosive popularity. Manually acquiring data at regular intervals is time-consuming and labor-intensive; therefore, daily, scheduled, and quantitative automated data acquisition and storage are essential. A key challenge in achieving robust data acquisition, cleaning, noise reduction, and path analysis within the constraints of privacy compliance and platform policies is how to implement this technology effectively.

[0004] At the methodological level, information dissemination in real social media environments exhibits complex characteristics such as high timeliness, high concurrency, and cross-platform and cross-community involvement. A small number of key dissemination nodes, such as bridging nodes, early initiators, and cross-circle intermediaries, often determine the speed, scale, and public opinion trajectory of trending posts. Real-time identification and analysis of these nodes are prerequisites for building efficient public opinion guidance and coordinated response capabilities. Therefore, the system incorporates a cutting-edge innovation centrality algorithm—Cenc. Inspired by "centripetal force," CenC collaboratively models the local, semi-local, and global information of nodes: it uses node degree and its exponential term to characterize "quality," structural hole constraint coefficients to characterize bridging / intermediation relaxation, and kernel degree to characterize global position; it also introduces neighbor order and distance as attenuation factors, following the "three-degree influence principle," to comprehensively evaluate the attraction / driving effect within the range of third-order neighbors. In terms of identification results, CenC is more sensitive to bridging key nodes, i.e., structural hole fillers, which helps to locate the "hidden main axis" of cross-circle dissemination in the early stages.

[0005] In application, existing tools mostly focus on monitoring topic popularity and analyzing sentiment, lacking the integrated capability to form a closed loop encompassing "real-time data acquisition, temporal network construction, key node identification, propagation path tracing, and adversarial control simulation." Especially in the early stages of a trending post's lifecycle, it is necessary to quickly identify "key nodes" with high marginal impact potential under conditions of sparse data and high signal noise, and to dynamically update the identification results based on changes in the propagation trend. Infection simulations should be conducted using complex network propagation dynamics across various network structures. Furthermore, in large-scale and high-concurrency environments, computational efficiency, robustness, and interpretability must also be considered.

[0006] In summary, existing technologies still have shortcomings in real-time identification of key propagation nodes, refined tracing of propagation paths, and adversarial control simulation based on propagation dynamics in real-world social media scenarios. There is an urgent need for an engineered system capable of operating under multi-platform, heterogeneous, adversarial, and incompletely observable conditions, supporting real-time data acquisition and cleaning at the level of trending posts, construction of complex temporal networks and analysis of key nodes, and propagation simulation and effect evaluation, in order to improve the real-time identification and analysis capabilities of key propagation nodes in social networks. Summary of the Invention

[0007] In view of this, embodiments of the present invention provide a method and system for identifying and extrapolating multi-element fusion propagation nodes in online social networks. The aim is to establish an engineering system that, taking the Weibo platform as an example, analyzes key public opinion hot posts in the context of real social media, obtains real and real-time Weibo hot post forwarding information and related forwarding information, verifies and uses complex network-related methods and propagation dynamics models based on this Weibo forwarding data, identifies key forwarding users under hot post data, analyzes hot post propagation paths, and simulates information propagation adversarial control networks.

[0008] The technical solution of this invention is implemented as follows: This invention provides a method for identifying and extrapolating multi-element fusion propagation nodes in online social networks. Specifically, it includes: acquiring forwarding information from trending posts on social platforms; constructing a forwarding network topology based on this information, where nodes in the topology represent forwarding users and edges represent forwarding relationships between corresponding nodes; evaluating and ranking the importance of nodes in the topology based on a centripetal centrality algorithm to obtain a node importance ranking; and dynamically simulating the information propagation process based on a strategy simulation algorithm using the forwarding information from trending posts on social platforms to complete the propagation effect evaluation.

[0009] This application also provides an online social network multi-element fusion propagation node identification and deduction system. This system is applied to the online social network multi-element fusion propagation node identification and deduction method. The system includes: a network construction module, an importance ranking module, and a dynamic simulation module. The network construction module is used to acquire forwarding information from popular posts on social platforms and, based on this information, construct a forwarding network topology graph. Nodes in the network topology graph represent forwarding users, and edges represent the forwarding relationships between corresponding nodes. The importance ranking module is used to evaluate and rank the nodes in the forwarding network topology graph based on a centripetal centrality algorithm, obtaining a node importance ranking. The dynamic simulation module is used to dynamically simulate the information propagation process based on the forwarding information from popular posts on social platforms using a strategy simulation algorithm, thereby completing the propagation effect evaluation.

[0010] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following: 1. This invention acquires information on reposts of popular posts on social media platforms and constructs a reposting network topology with reposting users as nodes and reposting relationships as edges. It integrates multi-dimensional topological indicators such as node degree, structural hole constraint coefficient, and kernel degree using a centripetal centrality algorithm. Combining the three-degree influence principle and neighborhood decay mechanism, it accurately calculates the centripetal centrality evaluation index of nodes and ranks them by importance. Simultaneously, based on a strategy simulation algorithm, it incorporates parameters such as infection probability and recovery probability, dynamically executing iterative processes such as infection, recovery, and attack node removal starting from an initial infection set. It simultaneously generates the expected scale evolution and statistics on the number of infection sources, effectively avoiding interference from highly redundant nodes, accurately identifying key propagation nodes such as cross-layer bridging and core layers, clearly depicting the evolutionary laws of information propagation and the effects of intervention. This achieves real-time, accurate identification of important propagation nodes in social networks and scientific, interpretable evaluation of propagation effects, providing efficient and robust engineering support for public opinion guidance, risk prevention, and platform governance.

[0011] 2. By constructing an undirected graph information propagation network with forwarding users as nodes and forwarding associations as edges, based on core topological parameters such as the number of nodes, average degree, and adjacency matrix, the basic topological indicators such as the degree value (number of direct connections), structural hole constraint coefficient (degree of structural constraint), and kernel degree (global position level) of each node are accurately calculated. The shortest path distance is defined as the neighbor set of a preset order. Inspired by classical centripetal force, a centripetal force parameter is dynamically generated, which includes a quality term composed of node self-importance and structural hole looseness, a periodic term corresponding to the preset order, and a radius term corresponding to the global position of the network. Combined with the neighborhood decay coefficient that decreases with the order and the self-weight of the self-quality contribution, a centripetal centrality evaluation index is calculated. Then, each node is sorted in reverse order according to this index, thereby avoiding the problem of misjudging highly redundant nodes caused by single-dimensional evaluation. It accurately characterizes the cross-layer bridging ability, global kernel layer advantage, and neighborhood influence decay law of nodes, and thus realizes the accurate identification and scientific ranking of key nodes with high propagation potential and core influence in social networks.

[0012] 3. By designating nodes whose number of reposts in trending posts on social media platforms exceeds a threshold as the first node, and combining them with seed nodes selected by users to form an initial infection set, infection probability and recovery probability parameters are set. The node statuses of infected individuals, recovered individuals, attackers (non-transmissible), and susceptible individuals are clearly defined. The process iteratively executes the process of assessing the success rate of infection for susceptible individuals, determining the recovery status of infected individuals, and removing attacker nodes. The process is simultaneously archived to the system time stack to support replayable and interpretable operations. The expected scale evolution at each moment and the number of target infection sources are dynamically generated and statistically analyzed in real time. A soft isolation strategy that fits the actual platform is adopted (preserving the topology and only removing the status), thereby accurately depicting the dynamic evolution of information dissemination. The inhibitory effect of external intervention on dissemination is effectively incorporated, ensuring the traceability of the simulation process and its fit with the actual scenario. This achieves scientific dynamic simulation of the information dissemination process on social networks, quantitative evaluation of dissemination effects, and accurate prediction of potential risks, providing data support and strategic reference for public opinion guidance and dissemination intervention.

[0013] 4. The network construction module acquires information on reposts of trending posts on social media platforms and constructs a reposting network topology with reposting users as nodes and reposting relationships as edges. The importance ranking module integrates local, semi-local, and global multi-dimensional topology information based on the centripetal centrality algorithm to accurately assess and rank the importance of nodes. The dynamic simulation module uses a strategy simulation algorithm combined with a propagation dynamics model to dynamically extrapolate and evaluate the information propagation process. These three modules work together to form a closed-loop capability of data collection, node identification, and propagation simulation. This effectively solves the shortcomings of existing technologies in real-time identification of important propagation nodes, characterization of cross-circle propagation paths, and simulation of propagation intervention effects. It avoids the limitations of single-dimensional evaluation and static analysis, thereby achieving accurate and real-time identification of important propagation nodes in social networks and scientific and traceable evaluation of information propagation effects. This provides efficient and integrated engineering support for public opinion guidance and control, risk prevention and control, and platform governance. Attached Figure Description

[0014] Figure 1 This is a flowchart of the method for identifying and deducing multi-element fusion propagation nodes in online social networks provided in this embodiment of the invention; Figure 2 This is a design logic diagram of the background automatic capture of real-time Weibo hot topic data provided in an embodiment of the present invention.

[0015] Figure 3 This is a flowchart illustrating the usage of the online social network multi-element fusion propagation node identification and deduction system provided in this embodiment of the invention. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0017] It should be understood that the terminology used in the description of the various examples herein is for the purpose of describing the particular examples only and is not intended to be limiting. As used in the description of the various examples and in the appended claims, the singular forms “a” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise.

[0018] It should also be understood that the term "and / or" as used herein refers to and covers any and all possible combinations of one or more of the associated listed items. The term "and / or" describes an association between related objects, indicating that three relationships can exist; for example, A and / or B can represent: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this application generally indicates that the preceding and following related objects are in an "or" relationship.

[0019] It should also be understood that, in the various embodiments of this application, the sequence number of each process does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0020] It should also be understood that determining B based on A does not mean determining B solely based on A; it is also possible to determine B based on A and / or other information.

[0021] It should also be understood that the term “comprising” (also referred to as “includes”, “including”, “comprises” and / or “comprising”) as used in this specification specifies the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0022] It should also be understood that the term "if" can be interpreted as meaning "when" or "upon" or "in response to determination" or "in response to detection." Similarly, depending on the context, the phrases "if determination..." or "if detection [the stated condition or event]" can be interpreted as meaning "when determination..." or "in response to determination..." or "when detection [the stated condition or event]" or "in response to detection [the stated condition or event]."

[0023] This invention provides a method for identifying and extrapolating multi-element fusion propagation nodes in online social networks. For example... Figure 1 The flowchart shown is for a method of identifying and extrapolating multi-element fusion propagation nodes in online social networks. The processing flow of this method may include the following steps: obtaining forwarding information of popular posts on social platforms, and constructing a forwarding network topology graph based on the forwarding information. In the network topology graph, nodes are forwarding users, and edges are the forwarding relationships between corresponding nodes; evaluating and ranking the importance of nodes in the forwarding network topology graph based on the centripetal centrality algorithm to obtain the node importance ranking; and dynamically simulating the information propagation process based on the forwarding information of popular posts on social platforms using a strategy simulation algorithm to complete the propagation effect evaluation.

[0024] In the ranking of node importance, cross-sphere bridging, core layer location, and structural hole looseness are taken into consideration. Therefore, in the actual simulation results, many medium-degree nodes rank highly. These medium-degree but highly centripetal accounts are more likely to break through community boundaries and cause cross-sphere diffusion in actual social media public opinion scenarios. On the other hand, some highly-degree accounts that are not ranked at the top of the node importance ranking may be concentrated in a single cluster with high neighbor redundancy, resulting in low marginal diffusion efficiency at the network level.

[0025] In the strategy simulation based on SIR and node attacks, the attack / isolation prioritizes blocking the "next-generation spreader," eliminating a significant proportion of new infections at the end of the step, effectively reducing the effective reproduction number. When the attacking node coverage is At that time, under the approximation of the configuration model: ; This intuitively demonstrates how the strategy suppresses cascading diffusion.

[0026] In this embodiment, the present invention, through the organic integration and progressive implementation of multiple technical means, achieves the scientific quantitative identification of important propagation nodes in the propagation chain of hot posts on social platforms and the dynamic and accurate evaluation of information propagation effects. This provides solid and practical technical support for the analysis of social network propagation nodes, the study of information propagation patterns, and related public opinion management. Technically, it possesses significant advantages in authenticity, objectivity, and comprehensiveness. The method first obtains forwarding information of hot posts on social platforms, abstracting forwarding users as nodes and the forwarding relationships between users as edges, constructing a forwarding network topology that fits the actual propagation scenario. This accurately and intuitively restores the actual forwarding and propagation structure of hot posts in social networks, abandoning abstract analysis methods detached from the actual propagation chain. This provides a real and reliable network data foundation for subsequent node importance assessment and propagation effect simulation, ensuring the rationality of subsequent analysis results from the source. Then, relying on a centripetal centrality algorithm, the importance of nodes in the forwarding network topology is assessed and ranked. The scientific computational logic of the algorithm realizes the assessment of the importance of each forwarding user node. The quantitative analysis and ordered ranking of the centripetal influence and coreness of nodes in the propagation network can objectively and accurately measure the actual importance of each node in the propagation chain, avoiding the subjectivity and one-sidedness of manual evaluation, and efficiently screening out the core nodes with key influence in the propagation network. Finally, combined with real hot post forwarding information on social platforms, the information propagation process is dynamically simulated and the propagation effect is evaluated through strategy simulation algorithms. This breaks through the limitations of static node evaluation and realizes the simulation and dynamic analysis of the actual propagation process of hot posts in social networks. It can comprehensively and meticulously present the information propagation trend and effect performance under the participation of different nodes, while verifying and improving the results of node importance ranking. This ensures that the identification conclusion of important propagation nodes is not only supported by algorithms at the network structure level, but also dynamically verified at the actual propagation effect level. Ultimately, it realizes a closed-loop analysis of the entire process from propagation network structure construction to quantitative evaluation of node importance, and then to dynamic verification of propagation effect, which greatly improves the accuracy, scientificity and practical reference value of identifying important propagation nodes in social networks.

[0027] like Figure 2The diagram shown illustrates the design logic for automatically capturing real-time trending topics on Weibo. It uses the example of automatically capturing the top 3 trending topics on Weibo, and revolves around a timed and quantitative, tracking and retrospective collection mechanism: Six fixed capture times are set daily (7:00, 10:00, 13:00, 16:00, 19:00, 22:00) to continuously acquire the first pinned trending Weibo post under the top 3 trending topics. Regarding the data collection strategy, after the initial capture of each trending post's pinned post, two follow-up data collections are completed within 12 hours. All collected Weibo data is formatted and stored in the database. Simultaneously, the system marks the network status for a 6-hour retrospective after 12 hours, ensuring the integrity and timeliness of the trending post's dissemination data. This provides comprehensive and continuous data support for subsequently building a forwarding network and identifying key nodes.

[0028] Furthermore, based on the centripetal centrality algorithm, the importance of nodes in the forwarding network topology is evaluated and ranked. The specific steps for obtaining the node importance ranking include: constructing an information propagation network, which is represented by an undirected graph, where the nodes of the undirected graph are the set of nodes in the forwarding network topology, and the edges of the undirected graph are the set of edges in the forwarding network topology; the formula for the information propagation network is expressed as: In the formula, Let V be the set of nodes and E be the set of edges in an information propagation network. Based on the core topological parameters of the network, the basic topological indices of each node are calculated. These core parameters include the number of nodes, average degree, and adjacency matrix. The basic topological indices include degree, structural hole constraint coefficient, and kernel degree. The set of each node in the network and the nodes whose shortest path distance is a preset order is denoted as the neighbor set of each node. The shortest path distance is the number of shortest edges in the undirected graph connecting the nodes. Based on the basic topological indices and shortest path distances of each node, the centripetal parameters of each node are dynamically generated. These parameters include a quality term, a periodicity term, and a radius term. Inspired by classical centripetal force, the action parameters are: mass term, which is a combination of node self-importance and structural hole looseness; periodic term, which is the action path length and a preset order; radius term, which is the global position of the network; neighborhood attenuation coefficient, which is dynamically generated based on the shortest path distance; neighborhood attenuation coefficient, which decreases with the order; and centripetal action parameters of each node, which are used to balance the direct contribution of "self-mass" to the overall index according to the preset self-weight θ, θ∈[0,1]. The centripetal centrality evaluation index of each node is generated through comprehensive analysis. The nodes are sorted in reverse order according to the centripetal centrality evaluation index, and the result of the reverse sorting is the node importance ranking.

[0029] Among the core topology parameters, the number of nodes is the number of elements contained in the node set; the average degree is the ratio of twice the total number of edges contained in the edge set to the total number of nodes contained in the node set; and the adjacency matrix is ​​a matrix that indicates whether there is a forwarding association between any two nodes in the node set. The rows and columns of the adjacency matrix correspond one-to-one with the nodes in the node set. The rules for the values ​​of the elements in the adjacency matrix are as follows: if there is a forwarding association between a node in a row and a node in a column, the matrix element at the intersection of that row and column is 1; if there is no forwarding association between a node in a row and a node in a column, the matrix element at the intersection of that row and column is 0.

[0030] In this embodiment, the present invention significantly improves the adaptability, accuracy, and comprehensiveness of the centripetal centrality algorithm in assessing the importance of forwarding nodes in social networks through standardized modeling, multi-dimensional feature extraction, scope definition that conforms to the laws of propagation, and scientific parameter design and weight balancing. This makes the results of the quantitative assessment and ranking of node importance more consistent with the actual information propagation characteristics of social networks and the real role of nodes in the propagation chain, providing a scientific and reliable quantitative basis for subsequent propagation effect simulation and identification of important propagation nodes. This step first transforms the forwarding network topology into an undirected graph form of information propagation network standardized by the formula G=V,E, completing the standardized mathematical modeling of the forwarding propagation structure of social networks, laying the foundation for all subsequent... Topology parameter calculation and index analysis establish a unified and quantifiable analytical foundation, ensuring the logical rigor and repeatability of subsequent calculations. Based on core topology parameters such as the number of nodes, average degree, and adjacency matrix (using 0 and 1 to precisely represent the forwarding relationships between nodes), multi-dimensional basic topology indicators such as degree, structural hole constraint coefficient, and kernel degree are accurately calculated. From different dimensions such as node connectivity, positional value in the network structure, and core hierarchical attributes, the core structural characteristics of each node in the propagation network are comprehensively extracted and characterized, avoiding the one-sidedness of a single structural indicator in characterizing node features and making the analysis of basic node attributes more complete. Then, using the number of shortest edges in the undirected graph connecting nodes as the shortest path distance, according to pre-defined... By defining the order of each node's neighborhood set, the scope of the node's influence analysis is limited to an effective neighborhood that conforms to the actual propagation patterns of information in social networks. This avoids computational redundancy and evaluation bias caused by unlimited expansion of the neighborhood, while ensuring a complete consideration of direct and indirect propagation relationships around the node, making subsequent analysis of interactions between nodes more closely resemble real information propagation paths. Inspired by classical centripetal force, a centripetal effect parameter is dynamically generated by combining the basic topology indicators and shortest path distance of each node, incorporating quality, periodicity, and radius terms. The quality term integrates the node's self-importance and structural hole slackness to accurately quantify the node's core propagation capabilities; the periodicity term anchors the path length of the effect at a preset order; and the radius term accurately reflects the node's position within the surrounding network. The global position in the propagation network and the multi-dimensional parameter design make the characterization of the centripetal effect of nodes more closely match the actual centripetal influence characteristics of nodes in social networks, achieving accurate and three-dimensional quantification of the centripetal effect of nodes. At the same time, based on the shortest path distance, a neighborhood decay coefficient that decreases with the order is generated, which conforms to the objective law that the influence of information propagation in social networks gradually decreases as the propagation path extends. This makes the evaluation of the interaction between nodes in the neighborhood more consistent with the actual propagation scenario. Furthermore, by pre-setting self-weights, the direct contribution of self-quality to the overall evaluation index is flexibly balanced, which can be adapted to the propagation characteristics of different types of social platforms. This effectively avoids the problem of single-dimensional factors overly dominating the evaluation results and achieves a scientific balance between the core attributes of the node itself and the influence of the surrounding neighborhood.Finally, a multi-dimensional analysis was conducted by integrating the neighborhood decay coefficient, the centripetal effect parameters of each node, and the self-weights to generate a centripetal centrality evaluation index that allows direct comparison of each node. The nodes were then sorted in reverse order according to this index to obtain the node importance ranking results. This transforms the complex multi-dimensional and multi-factor characteristics of nodes into a unified quantitative index, making the node importance ranking results more objective, accurate, and directly persuasive. It completely eliminates the problems of incomparable indicators and strong subjectivity in traditional evaluation methods, ensuring the scientific validity and reliability of the final node importance ranking results.

[0031] Specifically, the steps for calculating the basic topology indicators of each node based on the core topology parameters within the information propagation network include: For any node in the node set, obtaining all element values ​​of the row containing that node according to the adjacency matrix, and using the sum of all element values ​​as the node's degree value, which represents the number of direct connections the node has in the information propagation network; For any node in the node set, the ratio of the direct connection strength between the node and its corresponding neighbor node to the node's degree value is used as the direct investment ratio of the node to its corresponding neighbor node, which reflects the proportion of the direct connection strength between the node and its corresponding neighbor node to the total connection strength of the node; Obtaining all common neighbor nodes that are connected to both the node and its corresponding neighbor node, and for each common neighbor node, calculating the node's investment in the common neighbor node. The relationship ratio and the relationship ratio of common neighbor nodes to a given neighbor node are calculated. The sum of the calculation results for common neighbor nodes is taken as the indirect investment ratio of the node through common neighbor nodes. The indirect investment ratio reflects the proportion of the indirect connection strength between the node and its corresponding neighbor nodes through common neighbor nodes to the total relationship of the node. For all neighbor nodes of the given node, the direct investment ratio and indirect investment ratio of the given node on each neighbor node are summed. The sum of the squares of the summation results for all neighbor nodes is then calculated to obtain the structural hole constraint coefficient of the given node. The structural hole constraint coefficient is used to represent the degree of structural constraint that the node is subject to in the network. For any node in the node set, the information propagation network is decomposed into a kernel. Based on the decomposition results, the kernel level of the given node is determined, and the kernel level is assigned to the given node. The kernel degree of a node is used to represent the global position of a node in an information propagation network.

[0032] In this embodiment, the present invention designs refined and standardized calculation logic that fits the topological characteristics of social network propagation networks by targeting three core indicators: degree value, structural hole constraint coefficient, and kernel degree. This enables a comprehensive and precise quantitative characterization of the local connectivity, structural constraint state, and global core level of each node in the information propagation network. The calculation results of the basic topology indicators are highly consistent with the structural characteristics of nodes in the actual propagation network, avoiding the bias of a single indicator. This provides real, reliable, and quantifiable core foundational data for the subsequent dynamic generation of centripetal effect parameters and the comprehensive calculation of centripetal centrality evaluation indices, from the perspective of indicator calculation. This ensures the scientific rigor, accuracy, and comprehensiveness of subsequent node importance assessments. The standardized calculation steps also make the indicator calculation process highly operable and reproducible, adaptable to different types of social network forwarding and propagation network scenarios. For degree calculation, this step directly relies on the adjacency matrix of the information propagation network, using the sum of all elements in the row containing any node as its degree value. The calculation logic is highly compatible with the topological characteristics of undirected graphs. The number of direct connections to a node is directly anchored through the quantitative representation of 0s and 1s in the adjacency matrix. This standardized calculation method avoids errors from manual statistics, accurately and objectively reflecting the importance of nodes in the propagation network. The local direct propagation connectivity in a broadcast network becomes a core indicator for characterizing the basic propagation structure attributes of nodes. Regarding the calculation of the structural hole constraint coefficient, this step breaks through the traditional one-sided analysis method that only considers direct node connections. First, it defines the direct input ratio by the proportion of the direct connection strength between a node and its neighboring nodes to its degree value, accurately reflecting the relative proportion of direct connection strength between a node and its neighboring nodes. Then, by mining the common neighboring nodes of a node and its neighboring nodes, it calculates the relationship ratios between a node and its common neighboring nodes, and between common neighboring nodes and their respective neighboring nodes, and sums them to obtain the indirect input ratio, accurately capturing the relationship between a node and its neighboring nodes. The proportion of indirect connections established through common neighbors to the total relationships between nodes fully restores the direct and indirect dual connection status between nodes and their neighbors. Finally, the structural hole constraint coefficient is obtained by summing the direct and indirect input ratios of all neighbor nodes and then performing a square sum operation. This scientific calculation logic accurately quantifies the degree of structural constraint on nodes in the propagation network, effectively identifying whether a node is located in a structural hole position in the network. Nodes in structural hole positions are key hubs for information propagation in social networks. The accurate calculation of this indicator provides a core quantitative basis for subsequent evaluation of the structural value and propagation hub role of nodes.For kernel degree calculation, this step moves beyond the analytical perspective of local connectivity features. Starting from the global topology of the information propagation network, it decomposes the entire network into kernels, determines the kernel level of any node based on the decomposition results, and uses this as the kernel degree. This accurately characterizes the node's global position and core level attributes within the entire information propagation network. The level of the kernel directly reflects the node's core position in the global propagation network and its influence on network stability and information propagation dominance. This extends the characterization of the node's basic topological features from local connectivity to the global structure, achieving a comprehensive analysis of the node's structural characteristics. Furthermore, the calculation of the three major indicators—degree value, structural hole constraint coefficient, and kernel degree—each has its own emphasis and is relatively balanced. The two methods complement each other: degree value focuses on the node's local direct connectivity, structural hole constraint coefficient focuses on the node's structural constraint state and structural hole value in the network, and kernel degree focuses on the node's core-level position in the global network. Through this refined calculation, a multi-dimensional and three-dimensional quantification of the node's basic topological characteristics is achieved. This allows the basic topological characteristics of each node to be fully represented by a set of complementary quantitative indicators, completely avoiding the one-sidedness of a single indicator in characterizing the node's structural characteristics. This ensures that the centripetal effect parameters generated based on these indicators can truly and comprehensively reflect the actual structural characteristics of the node in the propagation network, laying a solid core data foundation for the final accurate assessment and ranking of node importance.

[0033] Specifically, the method for obtaining the centripetal centrality evaluation index of each node is as follows: ; In the formula, This represents the centripetal centrality evaluation index of the i-th node. For the weight of the item, For the quality item of the i-th node, Where e is the natural constant, a is the equilibrium coefficient, and a = 10. -n 'n' represents the order of magnitude of the network, to avoid excessive self-importance of nodes (reflected by their degree values) when calculating quality. The degree value of the i-th node. , Let i represent the value of the element in the i-th row and j-th column of the adjacency matrix, where i and j are node numbers, and i ≠ j, i = 1, 2, 3, ... |V|, j = 1, 2, 3, ... |V|, and |V| is the number of nodes in the core topology parameters. Suppress the order-of-magnitude imbalance of degree values ​​under network size differences; Let be the structural hole constraint coefficient of the i-th node. , This represents the proportion of direct investment made by node i in its neighbor node j. This indicates that node i is connected to its common neighbor nodes. The proportion of indirect input with neighbor node j, ; , This represents the common neighbor node of node i and its neighbor node j, that is, the intermediate node that connects both i and j. This indicates that node i has joined the common neighbor nodes. The proportion of relationships to the total relationships of node i. Represents common neighbor nodes The relationship invested in node j accounts for the node The proportion of total relationships Strengthen the structural tunnel-bridge connection nodes; The m-th order neighborhood attenuation coefficient, m is the order, m=1,2,3, following the three-dimensional influence principle, reflecting that the "three-dimensional influence" decreases with the order; Let d(i,j) be the set of m-order neighbors of the i-th node, where d(i,j) is the shortest path distance and d(i,j) = m, representing the periodic term. Characterizing distance-dependent attenuation matches the physical meaning of "inverse square of period"; For the kernel degree of the j-th node, i.e. the radius term, in the summation formula, this term describes the attribute of the neighbor object j attracted or influenced by the central node i, projecting the global "kernel potential" of the neighbors into the "radius" contribution.

[0034] In this embodiment, the present invention designs a centripetal centrality evaluation index calculation formula that integrates multi-dimensional core parameters, conforms to the propagation law of social networks, and has undergone targeted optimization. It scientifically integrates and coordinates key quantitative indicators such as self-item weight, node quality item, multi-order neighborhood decay coefficient, neighborhood node kernel degree, and shortest path distance, achieving standardized, accurate, and comprehensive quantitative calculation of node centripetal centrality. This ensures that the final evaluation index highly reflects the actual characteristics of information propagation in social networks, truthfully and objectively reflecting the actual centripetal influence and core propagation value of each node in the propagation network. Simultaneously, the design of each parameter and the calculation logic of the formula are adapted to the topological characteristics and propagation law of social networks, effectively avoiding evaluation biases caused by differences in network scale, distance decay, and single-dimensional dominance. It achieves a scientific balance between node self-attributes and neighborhood influence, local structural features and global topological attributes, and direct propagation capability and structural hub value. This provides a unified, comparable, and highly reliable quantitative basis for subsequent reverse ranking of node importance by index, significantly improving the adaptability, accuracy, and scientific nature of the centripetal centrality algorithm in evaluating the importance of propagating nodes in social networks from the core calculation level.The self-weight θ setting allows for flexible adjustment of the direct contribution of the node's own quality item to the evaluation index. The weight ratio can be adjusted according to the propagation characteristics of different social platforms, adapting to diverse network propagation scenarios and avoiding the problem of a single dimension excessively dominating the evaluation results due to the influence of the node's own attributes or neighborhood. The calculation formula for the quality item has undergone multi-dimensional refinement. First, by balancing coefficients and exponential operations, it effectively suppresses the order-of-magnitude imbalance of degree values ​​under different network sizes, making the calculation of node quality items in social networks of different sizes comparable. The degree value is precisely quantified by summing the elements of the adjacency matrix, laying a real structural foundation for the quality item. Then, through reverse reinforcement design, the quality item is strengthened by bridging structural holes and constraining coefficients. Nodes with smaller values ​​receive higher weights in the quality item, accurately highlighting the pivotal value of structural hole nodes in information dissemination. This achieves a quantified integration of node direct connectivity and structural hole pivotal attributes, allowing the quality item to comprehensively reflect the node's core dissemination value. The m-order neighborhood decay coefficient follows the three-degree influence principle, with m=1,2,3. The decay coefficient decreases as the order increases, precisely aligning with the objective law that the influence of information dissemination in social networks gradually diminishes as the dissemination path extends. Simultaneously, the three-degree influence principle limits neighborhood analysis to the effective range of information dissemination, avoiding computational redundancy and evaluation bias caused by unlimited expansion of the neighborhood. The m-order neighbor set is precisely matched with the shortest path distance, strictly defining the neighborhood range as the distance to node i. The set of nodes with a path distance of m ensures the accuracy of neighbor node selection, closely aligning with real information propagation paths. The inverse square law design, drawing on physical principles, further enhances the distance-based attenuation effect, making the contribution of neighboring nodes farther from node i smaller to the evaluation index, better reflecting the characteristic that influence weakens with distance in actual propagation. Incorporating the kernel degree of neighboring node j as a radius term into the summation formula further projects the global kernel level attribute of neighboring nodes as a radius term contribution to the evaluation index of node i. This ensures that the centripetal centrality evaluation of node i considers not only its own attributes and connections with neighboring nodes but also the global core value of neighboring nodes, accurately reflecting the node's ability to attract and influence core nodes in the propagation network, thus achieving [the desired effect]. The system deeply integrates local neighborhood features and global topological attributes. The overall formula sums the neighborhood terms according to the m-th order, integrating the comprehensive contributions of neighborhood nodes from the 1st to the 3rd order. It comprehensively considers the direct and indirect neighborhood influence of nodes, enabling the calculation of the entire evaluation index to achieve multi-dimensional integration of its own core attributes, neighborhood influence, distance decay, and global attributes. It successfully transforms the complex structural characteristics and diverse propagation values ​​of nodes in the propagation network into a unified quantitative index, allowing the centripetal centrality of different nodes to be directly and objectively compared through the evaluation index. This completely eliminates the problems of fragmented, incomparable, and highly subjective indicators in traditional evaluation methods, ensuring that the calculated evaluation index can serve as a scientific and reliable basis for ranking the importance of nodes.

[0035] Furthermore, based on the forwarding information of popular posts on social media platforms, the steps for dynamically simulating the information dissemination process using a strategy simulation algorithm include: designating nodes whose forwarding frequency exceeds a preset forwarding threshold as the first node; obtaining a preset set of probability parameters, including infection probability and recovery probability, both of which are within the (0,1) interval; designating the set of the first node and preset seed nodes as the initial infection set, where seed nodes are the nodes selected by the user in the console; obtaining the status of each node, including infected, recovered, attacker, and susceptible, where a node in the attacker state will not infect other nodes; S1: For nodes in the susceptible state, dynamically evaluate based on the infection probability. S1: Estimate the probability of successful infection for each susceptible individual, and denot the node that becomes an infected individual based on the probability of successful infection as an infected individual; S2: For nodes in the state of infected individual, denot the node that becomes a recovered individual based on the probability of recovery as a recovered individual; S3: Remove nodes in the state of attacker from the infected individual set; S4: Remove nodes in the state of attacker from the recovered individual set; Repeat steps S1-S4 and save them to the system time stack, supporting "previous step / next step / rollback" operations to ensure replayability and interpretability; Dynamically generate the expected scale evolution at each time step based on the node state at each time step; Real-time statistics of the number of nodes successfully infected by the infection source are recorded as the target number of each infection source, where the infection source is the node in the susceptible individual's neighbor set that is in the state of infected individual.

[0036] In this embodiment, the attacker's node can be exposed and reached but will not become a source of propagation in the next step, and will not participate in the subsequent infection and recovery accumulation process, effectively reducing the effective regeneration number. The system supports two strategies: "hard deletion" to remove nodes and their edges, and "soft isolation" - state-only removal, preserving the graph topology. Soft isolation is used by default, which is more in line with the actual handling of platform rate limiting, muting, etc. This invention achieves highly accurate, controllable, and adaptable dynamic simulation of the spread of trending topics on social networks by employing node selection tailored to the actual dissemination scenarios of social platforms, multi-dimensional probability parameter configuration, phased dynamic evolution design of node states, traceable simulation process control, and a dual isolation strategy adapted to the actual handling needs of the platform. It can accurately capture changes in node states, the evolution of dissemination scale, and the actual dissemination effectiveness of each source of infection at each moment of information dissemination. This provides dynamic, verifiable, and realistic quantitative data support for a comprehensive and accurate evaluation of dissemination effects. Simultaneously, it makes the simulation process replayable, interpretable, and controllable, thus overcoming the limitations of static node importance assessment. It can also reverse-verify and improve the previous node importance ranking results and is highly adaptable to the actual operational and handling scenarios of social platforms, significantly improving the practical applicability and application value of the entire important dissemination node identification method. The initial infection set is created by combining the first node with a preset threshold of forwarding counts with user-selected seed nodes. This anchors the core initial nodes with high forwarding capabilities in actual social media dissemination while retaining the flexibility for users to customize the simulated starting point based on actual analysis needs. This ensures that the simulated initial propagation nodes more closely resemble the characteristics of real hot post propagation starting points, guaranteeing the authenticity of the propagation process simulation from the source. The preset intervals for infection and recovery probabilities form a set of probability parameters. Nodes are categorized into four states: infected, recovered, attacker, and susceptible. Attacker nodes are specifically designed to be accessible but not become a source of propagation, do not participate in subsequent infection and recovery accumulation processes, and effectively reduce the effective reproduction number. This range-based setting of probability parameters ensures that the simulation of the infection and recovery process closely matches the information dissemination process in social networks. The random and objective laws avoid simulation bias caused by absolute propagation judgments. Furthermore, by setting exclusive states for attacker nodes, it accurately restores the platform's handling characteristics of violating and traffic-limiting nodes in actual propagation, making the division of node states more consistent with real social network propagation scenarios. The design of phased dynamic evolution steps of node states from S1 to S4 first dynamically assesses the probability of successful infection of susceptible individuals based on the probability of infection and updates them to infected individuals. Then, infected individuals are updated to recovered individuals based on the probability of recovery. Subsequently, attacker nodes are removed from the sets of infected individuals and recovered individuals in real time. Through this phased evolution logic that conforms to the natural laws of information propagation, the state changes of the entire propagation process from susceptible individuals to infected individuals and then to recovered individuals are accurately restored. The real-time removal of attacker nodes ensures the accuracy and timeliness of node states during the simulation process and avoids interference from invalid nodes with the propagation simulation results.The simulation process is repeatedly executed and saved to the system time stack, supporting "previous step / next step / rollback" operations. This enables full-process data retention and operation backtracking for the entire dynamic simulation of information dissemination, completely solving the pain points of traditional dissemination simulation processes, such as lack of traceability, difficulty in identifying simulation deviations, and lack of interpretability of results. It gives the simulation process replayability and interpretability, facilitating subsequent analysis and verification of dissemination patterns. Based on the node status at each moment, the expected scale evolution is dynamically generated, while the number of nodes successfully infected by each infection source is counted in real time as the target number. This transforms the dynamic simulation process data into precise quantitative evaluation indicators. The expected scale evolution can intuitively and clearly present the dynamic changing trend and evolutionary pattern of the information dissemination scale at different moments, while the target number of infection sources precisely quantifies each... The actual propagation efficiency of the infection source provides a direct and comparable quantitative basis for analyzing the actual propagation capabilities of different nodes (especially important propagation nodes identified in the early stages), enabling a precise and comprehensive evaluation of the propagation effect. Simultaneously, two isolation strategies are designed: hard deletion (removing nodes and their edges) and soft isolation (only removing states and preserving the graph topology), with soft isolation being the default. This dual-strategy design allows the simulation algorithm to adapt to different node handling needs on social platforms. Hard isolation is suitable for extreme scenarios requiring the complete removal of nodes, while soft isolation closely aligns with common platform operations such as traffic limiting and muting, which only restrict node propagation capabilities without deleting nodes or topological relationships. This ensures a high degree of consistency between the simulation strategy and actual platform operations, significantly improving the algorithm's practical application adaptability and feasibility.

[0037] Specifically, the method for obtaining the success rate of infection for each susceptible individual is as follows: ; In the formula, This represents the probability of successful infection in the v-th susceptible individual. The set of neighbors of the v-th susceptible individual is equivalent to the set along each line. Each individual undergoes a β-Bernoulli experiment independently; if successful, they are added to the new infection pool. For the probability of infection, Let be the set of infected individuals at time t, and v be the ID of each susceptible individual, v = 1, 2, 3, ... , Let t be the set of susceptible individuals. , For those recovering at time t, Let u be the set of nodes, where u = 1, 2, 3, ... , Let V be the set of neighbors and infected persons of the v-th susceptible person at time t.

[0038] In this embodiment, the present invention designs a standardized calculation formula for the success probability of infection that aligns with the random independence of information propagation in social networks and the synergistic influence of multiple infection sources. This formula scientifically integrates and logically calculates key dynamic parameters such as infection probability, the real-time neighbor set of susceptible individuals, and the set of infected individuals at each time point. This achieves accurate, objective, and dynamic quantitative calculation of the success probability of infection for each susceptible individual at time t. It provides a unified, scientific, and reproducible probability determination basis for the evolution of susceptible individuals into infected individuals in the propagation process simulation. This ensures that the infection stage of the information propagation simulation closely matches the actual propagation patterns in social networks, where information spreads through multiple independent links and susceptible individuals are influenced by the synergistic effects of surrounding infection sources. It effectively avoids simulation deviations caused by single infection source determination, fixed probability assignment, and interference from invalid nodes. From the core probability calculation level, it significantly improves the realism, accuracy, and scientific rigor of the entire dynamic simulation of the information propagation process. At the same time, the concise calculation logic and standardized parameter calls of the formula also ensure the computational efficiency and verifiability of the simulation results.This approach treats the transmission links between susceptible individuals and each infected neighbor as independent Bernoulli experiments, precisely aligning with the reality in social networks where information spreads to susceptible individuals through different friend links without interference. By subtracting the product of the probabilities of unsuccessful infection from each independent transmission link (1), it scientifically quantifies the actual probability of successful infection for susceptible individuals when multiple infected sources coexist. This overcomes the limitations of traditional single-source infection probability determination, realistically recreating the transmission scenario in social networks where a susceptible node is often simultaneously influenced by multiple surrounding infected sources, making the calculation of infection probability more comprehensive and practically relevant. It accurately identifies nodes in the susceptible individual's neighbor set that are actually infected at time t, only those nodes related to the susceptible individual. By including infected neighbors with actual infectivity in the probability calculation, interference from invalid entities such as non-neighbor nodes and non-infected nodes is completely eliminated. This ensures that the calculation of the infection success probability is highly synchronized with the real-time transmission scenario at time t. It strictly adheres to the transmission characteristic of social networks, where susceptible individuals can only be affected by directly related infected sources in their vicinity, guaranteeing the timeliness and accuracy of infection probability calculations for different susceptible nodes at different times. The scope of the susceptible population at time t is precisely defined, clarifying that the sole calculation object for the infection success probability is the node that is not currently infected or recovered. Furthermore, a unique number is assigned to each susceptible individual, and the calculation scope is limited, achieving standardized and precise definition of the calculation object and preventing the inclusion of non-susceptible nodes from the outset. The inclusion of probability deviations caused by calculations ensures the accuracy of the probability calculation. The infection probability in the formula is a preset parameter within the (0,1) interval, which can be flexibly adjusted according to the information dissemination characteristics of different social media platforms, allowing the probability calculation formula to adapt to different types of social network dissemination scenarios, possessing good scenario adaptability and flexibility. Furthermore, all parameters in the formula are derived from dynamic quantitative indicators during the dissemination simulation process. The infection probability β is a pre-set core parameter based on the node neighbor set of the information dissemination network topology and the real-time updated set of infected and recovered individuals. Through real-time calling and calculation of these dynamic parameters, the formula achieves dynamic calculation of the infection success probability, allowing for accurate determination of the infection probability of each susceptible individual. The probability can be adjusted in real time as the transmission process progresses and the node status changes, which closely matches the dynamic evolution of node status during information transmission. This allows the simulation of the entire infection process to be accurately updated dynamically following the changes in the transmission process. At the same time, the calculation logic of the entire formula is based on classic set operations and probability product rules, without any subjective assignment. All parameters come from core indicators that have been standardized and quantified in the early stage. The standardized calculation logic provides a unified judgment standard for calculating the probability of successful infection for different susceptible individuals at different times. This not only ensures the objectivity and reproducibility of the probability calculation results, but also makes the calculation logic of the formula simple and easy to understand, greatly improving the calculation efficiency of the simulation process and facilitating the subsequent verification and analysis of the simulation results.The successful design of this formula upgrades the determination of infection status in the transmission simulation from qualitative description to quantitative and precise calculation, providing core quantitative support for the implementation of step S1. It makes the transformation of susceptible individuals into infected individuals more in line with the actual transmission pattern, thereby ensuring the authenticity and accuracy of the dynamic simulation of the entire information transmission process. It also lays a reliable computational foundation for subsequent transmission effect evaluation work such as generating expected transmission scale evolution and statistical analysis of the transmission effectiveness of infection sources.

[0039] Specifically, the expected scale evolution at each time step is obtained as follows: ; In the formula, Let be the number of nodes that are already infected at time t. This represents the probability of a single infected node infecting its neighboring susceptible nodes in a single instance. The recovery rate is the probability that a node in an infected state at time t will recover by time t+1. , represents the number of infected neighbors of node v at time t. The loss term is the external intervention, specifically the reduction in the infection scale caused by external factors (such as prevention and control measures, natural losses, etc.) at time t. It reflects the reduction of the infected scale by the attack projection and is approximately related to the probability of the infected target falling into A and the attack intensity.

[0040] In this embodiment, the present invention achieves accurate, dynamic, and multi-dimensional quantitative prediction of the evolutionary trend of information spread and infection scale at each moment by designing a standardized formula for calculating the expected scale of spread that integrates core dynamic parameters of propagation, natural evolution laws, and external intervention influences. This transforms the node state evolution process of propagation simulation into quantifiable, comparable, and analyzable infection scale trend indicators, upgrading the assessment of propagation effect from simple node state statistics to trend prediction and factor analysis. This provides a scientific quantitative basis for accurately judging the laws of information spread and can also verify the accuracy of identifying important propagation nodes in the early stages. At the same time, it is highly adaptable to the actual propagation control needs of social platforms, greatly improving the depth, practicality, and practical reference value of propagation effect assessment, and consolidating the evaluation core of the strategy simulation algorithm from the perspective of scale quantification. The formula uses the actual number of infected nodes at time t as the basic calculation base, directly anchoring the real-time infection scale at each time point in the propagation simulation. This ensures that the calculation of the evolutionary expectation starts from the real propagation state, strictly adhering to the real-time characteristics of dynamic simulation, and completely avoiding abstract assignments detached from the actual propagation process. This guarantees the authenticity and relevance of the scale evolutionary expectation calculation results from the source. By deeply binding the infection expectation of a single susceptible node with the actual propagation scenario, where the number of infected neighbors of node v at time t accurately quantifies the actual infection risk faced by each susceptible node, it aligns with the objective propagation law in social networks where susceptible nodes are affected by the synergistic influence of surrounding infection sources, and the higher the number of infected neighbors, the higher the infection probability. Combined with the single infection probability, the infection expectation calculation of susceptible nodes under multiple infection sources is completed. Finally... By summing up the expected overall increase in the conversion of all susceptible individuals to infected individuals at the next moment, the core growth logic of the infection scale in information dissemination is scientifically restored. This breaks through the one-sidedness of the traditional model that assigns a fixed infection probability to all susceptible nodes, making the calculation of the infection increment more accurate and more in line with the actual characteristics of dissemination. The formula incorporates the calculation of the recovery term, multiplying the recovery rate by the number of infected nodes at time t, which accurately quantifies the expected reduction in the conversion of infected individuals to recovered individuals at the next moment due to natural factors such as the decline in the heat of information dissemination and the loss of the willingness to spread. This truly restores the natural evolution law of information dissemination, and achieves a scientific balance between the expected increase in infection and the expected reduction in natural recovery. The calculation of the expected scale evolution takes into account both the trend of dissemination and the characteristics of dissemination attenuation, and fully presents the natural evolution process of information dissemination.The formula innovatively introduces an external intervention loss term, quantifying external influencing factors in the actual spread control of social media platforms, such as prevention and control measures, platform traffic limiting and soft isolation, and attacker node handling. This accurately depicts the actual reduction effect of external intervention on the scale of infection. Furthermore, it clarifies that this loss term is related to the probability of the infected target falling into the attacker set and the attack intensity, deeply echoing the attacker node setting and soft isolation / hard deletion strategy in claim 6. This breaks through the limitations of traditional spread evolution models that ignore external intervention and only consider natural spread laws, allowing the scale evolution expectation to truly reflect the impact of external factors such as human control and platform handling during actual spread, highly adaptable to the actual spread control scenarios of social media platforms. In addition, all calculation parameters in the formula are derived from dynamic quantitative indicators or flexibly adaptable preset parameters during the spread simulation process, and the parameters are updated in real time with the evolution of node states in the spread simulation. It can accurately match the changes in the transmission scenario at each moment. The infection probability and recovery rate are adaptable parameters that can be flexibly adjusted according to the transmission characteristics of different social platforms. The external intervention loss can be dynamically quantified according to the actual control measures and the number of attacker nodes. The dynamism and adaptability of all parameters make the formula applicable to the simulation of the spread of hot posts on social networks in different types and transmission scenarios, with strong scenario adaptability and flexibility. At the same time, the formula follows the progressive calculation logic of basic infection scale, expected increase in susceptible conversion, expected decrease in natural recovery, and expected decrease in external intervention. It organically integrates the basic transmission state, infection spread law, natural decay characteristics, and external intervention impact on the infection scale during the information transmission process, and realizes a comprehensive and systematic quantitative calculation of the infection scale evolution at the next moment. This allows the final expected scale evolution to fully and accurately reflect the actual evolution trend of the infection scale at each moment.The standardized formula design also makes the calculation of the expected scale evolution highly objective, reproducible and efficient. All parameters are derived from the indicators that have been quantified in the previous simulation process, without any subjective assignment, which ensures the uniformity of the calculation standard in different scenarios and simulation processes. At the same time, the simple calculation logic takes into account both calculation accuracy and real-time performance, and can quickly generate the expected scale evolution at each time point in the repeated iteration of propagation simulation, adapting to the real-time calculation needs of dynamic simulation. This formula successfully integrates "refined evolution of node states" and "precise prediction of propagation scale," enabling the strategy simulation algorithm not only to recreate the node state change process of information propagation but also to quantitatively predict and analyze the dynamic trend of propagation scale. By comparing the number of nodes already in an infected state at different times, the diffusion and attenuation trends of information propagation can be intuitively judged. By analyzing the impact of parameter changes on evolution expectations, the effect of each factor on propagation scale can be accurately quantified. Furthermore, by simulating the expected changes in scale evolution when different important propagation nodes are the initial infection sources, the accuracy of the previous node importance ranking can be verified in reverse. At the same time, it provides a quantitative reference for the actual propagation control of social platforms. By simulating the loss terms and expected scale evolution under different external intervention intensities, optimal handling strategies such as traffic limiting, muting, and soft isolation can be formulated. This makes the propagation effect evaluation of the multi-element integrated propagation node identification and inference method in online social networks more in-depth and practically valuable, and makes the final identification results and propagation control recommendations more scientific and implementable.

[0041] Specifically, the target number for each source of infection is obtained as follows: ; In the formula, For the target number of the u-th infection source, Let t be the number of nodes successfully infected by the infection source. For the neighbor set of the uth infected person, To establish the association between the source of infection u and the susceptible individual v, For the source of infection u edge The point at which infection is successful.

[0042] In this embodiment, the present invention, by designing a recursive formula for calculating the target number of infection sources that aligns with the dynamic evolution characteristics of information dissemination, achieves accurate, real-time, and continuous quantitative statistics on the number of nodes successfully infected by each infection source throughout the entire dissemination process. This shifts the overall dissemination effect assessment from macroscopic scale evolution analysis to microscopic single-node dissemination capability assessment, making the dissemination effect assessment more refined, targeted, and practical. It provides direct, comparable, and highly reliable quantitative evidence for accurately identifying the actual dissemination value of each infection source, bidirectionally verifying the results of identifying important dissemination nodes in the early stages, and formulating differentiated social media platform dissemination control strategies. At the same time, it makes the evaluation system of the strategy simulation algorithm more complete, forming a deep logical closed loop with the entire important dissemination node identification method, significantly improving the scientific nature and practical application value of the method. The formula employs a recursive calculation logic, dynamically updating the target number of each infection source in real time by continuously accumulating data as the propagation simulation S1-S4 iterates. This accurately records the number of nodes successfully infected by each infection source throughout the entire propagation cycle, enabling full-process, dynamic tracking and statistics of the transmission effectiveness of infection sources. This completely avoids the problem that traditional single-time statistics cannot reflect the dynamic changes in the effectiveness of infection sources during the propagation process, allowing the target number to truly and completely reflect the cumulative transmission contribution of infection sources in the actual propagation process. At the same time, the recursive calculation logic is simple and efficient, and can quickly complete real-time calculations during simulation iterations. It is compatible with the "previous step / next step / rollback" operations of the system time stack, allowing the target number statistics to be synchronously traced back with the propagation simulation process. It has the characteristics of being replayable and interpretable, facilitating subsequent review and analysis of the propagation process of core infection sources. The formula precisely anchors the nodes in a susceptible state within the neighbor set of the infection source at time t. It only includes susceptible neighbors that the infection source can influence through direct adjacency links in the statistical scope of successful infection, strictly adhering to the objective law of information propagation through direct relationships in social networks. This completely eliminates interference from invalid objects such as non-neighbor nodes and non-susceptible nodes, ensuring the accuracy and rationality of the target number calculation for each infection source from a statistical perspective. This allows the target number to truly reflect the actual transmission and radiation capacity and effective influence range of the infection source. This invention precisely focuses on the independent transmission links between the infection source and susceptible individuals, clearly defining nodes where the infection source successfully infects along exclusive associations. It effectively avoids the statistical confusion problem when multiple infection sources simultaneously infect the same node, clearly defining the actual infection results of each infection source. This allows for absolute direct comparison of the target numbers of different infection sources, facilitating the rapid and intuitive selection of the core infection source with the highest transmission efficiency. It also enables precise analysis of the efficiency of a single transmission link for different infection sources, providing refined data support for mining the transmission characteristics of core infection sources.Meanwhile, the number of infection sources calculated by this formula, as a core quantitative indicator of the actual transmission effectiveness of a single node, can form a logical closed loop of two-way verification with the node importance ranking obtained through the centripetal centrality algorithm in the early stage: if the important transmission nodes identified by the algorithm in the early stage show a higher number of targets in the transmission simulation, it indicates that the node importance ranking result is highly consistent with the actual transmission scenario and has practical rationality; if some nodes are ranked high in the algorithm but have a low number of targets in the simulation, the parameter settings and evaluation logic of the centripetal centrality algorithm can be optimized in reverse based on the transmission links, infection range and other data behind the number of targets, so that the entire important transmission node identification method forms a complete closed loop of "algorithm evaluation-simulation verification-reverse optimization", which greatly improves the scientificity and reliability of the final node identification result. Furthermore, from the perspective of actual operation and management on social media platforms, the target number of each infection source provides a precise quantitative basis for transmission control. The transmission effectiveness of infection sources can be graded according to the target number value. For core infection sources with high target numbers, high-intensity control strategies such as soft isolation and hard deletion are prioritized, while ordinary infection sources with low target numbers are subject to conventional monitoring strategies. This achieves differentiated and precise control of transmission nodes, making the platform's traffic restriction and banning measures more targeted and effective. It avoids the waste of resources caused by indiscriminate control, is highly adapted to the actual transmission control needs of social media platforms, and allows the technical achievements of the entire important transmission node identification method to be directly implemented into the platform's practical strategy, greatly enhancing the practical application value of the method.

[0043] like Figure 3 The flowchart shown is for the use of an online social network multi-element fusion propagation node identification and inference system. This system includes: a network construction module, an importance ranking module, and a dynamic simulation module. The network construction module acquires forwarding information from popular posts on social platforms and constructs a forwarding network topology based on this information. Nodes in the network topology represent forwarding users, and edges represent the forwarding relationships between corresponding nodes. The importance ranking module evaluates and ranks the nodes in the forwarding network topology based on a centripetal centrality algorithm, obtaining a node importance ranking. The dynamic simulation module dynamically simulates the information propagation process based on the forwarding information from popular posts on social platforms using a strategy simulation algorithm, thus completing the propagation effect evaluation.

[0044] Take the Weibo post by user "Mr. CarEngineer" about "Xiaomi spontaneous combustion on Tianfu Avenue" published on October 13, 2025 as an example. The Weibo shows 364 retweets, and the system captured 348 valid retweets, with a data coverage rate of approximately 95.6%, falling within the range of 90% - 100%, which can represent the real dissemination structure. Sort the same data according to "degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality" respectively, and uniformly select the user ranked 7th in each index as the initial infection source, and set the SIR parameters: simulation rounds 3, maximum time step 10, infection rate β = 0.5, recovery rate γ = 0.2. The average dissemination scale obtained is as follows: The comparison results show that under the same initial conditions and parameter settings, eigenvector centrality performs best in the average dissemination scale of three repetitions: compared with degree centrality, it increases by approximately 97.6%; compared with closeness centrality, it increases by approximately 62.1%; compared with betweenness centrality, there is still an increase of approximately 2.1%. In the short-term dissemination window with limited steps and a relatively high infection rate, eigenvector centrality can more effectively select seed nodes with both "cross-layer bridging ability" and "global core layer advantage", enabling it to break through the community boundary faster in the early stage and cover more valid nodes within the same time step.

[0045] The multi-factor integration of eigenvector centrality brings the advantage of "effective early coverage". When sorting, it simultaneously considers the local connection strength of nodes, the structural hole slackness), as well as the core layer position and performs distance attenuation on the contribution of high-order neighbors, thereby balancing the weights of "strongly connected nodes" and "cross-layer hubs". In this case, the 7th node selected by eigenvector centrality has strong cross-community reach ability, and can push the infection front to more different local clusters in the first few steps, resulting in a larger cumulative scale within the same time step. Compared with degree centrality, nodes with high degree but large neighbor redundancy are prone to have the diffusion limited within a single cluster, with low marginal coverage efficiency; eigenvector centrality effectively avoids such "high-redundancy seeds" through structural holes and core layer information; compared with betweenness centrality, betweenness emphasizes the shortest path but does not explicitly characterize the potential advantage of nodes located in the core layer, resulting in not necessarily being able to convert into a larger actual infection in the short-term diffusion window. The incorporation of the core layer position by eigenvector centrality brings a small advantage in this case; compared with closeness centrality, closeness centrality tends to select nodes with short average distance, but the attenuation and bridging nature of high-order neighbors are not well characterized, and it is easy to select candidates that are "close" in the local structure but have limited "cross-layer propagation ability". The average dissemination scale of eigenvector centrality is significantly higher.

[0046] For control and guidance, on the propagation side, selecting initial seeds based on centripetal centrality sorting more closely approximates the upper bound of actual cross-circle diffusion, which can be used to assess potential risks and platform load. On the control side, using the centripetal centrality Top-k as attack / isolation targets on the same network can more effectively cut off cross-community propagation chains, theoretically reducing the effective number of regenerators and delaying or suppressing peaks. Compared to the same amount of cleanup based on degree, proximity, and betweenness, this method offers higher suppression strength and better resource efficiency. Combined with a seed exclusion (SE) strategy, redundancy can be further reduced, improving the cost-effectiveness of peak suppression and scaling down with limited disposal capacity. This system allows for low-cost, repeated experimental testing.

[0047] The program code used to implement the methods of this disclosure may be written in any combination of one or more programming languages. This program code may be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing apparatus, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code may be executed entirely on a machine, partially on a machine, as a standalone software package partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0048] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor); and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the computer. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0049] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as a data server), or computing systems that include middleware components (e.g., an application server), or computing systems that include frontend components (e.g., a user computer with a graphical user interface or web browser through which a user can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., a communication network). Examples of communication networks include local area networks (LANs), wide area networks (WANs), and the Internet.

[0050] Computer systems can include clients and servers. Clients and servers are generally located far apart and typically interact through communication networks. The client-server relationship is created by computer programs running on the respective computers and having a client-server relationship with each other.

[0051] The above description is only an optional embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for identifying and extrapolating multi-element fusion propagation nodes in online social networks, characterized in that, The method includes: Obtain information on the forwarding of popular posts on social media platforms, and construct a forwarding network topology based on the forwarding information. In the network topology, nodes represent forwarding users, and edges represent the forwarding relationships between corresponding nodes. The importance of nodes in the forwarding network topology is evaluated and ranked based on the centripetal centrality algorithm, resulting in a node importance ranking. Based on information forwarded from trending posts on social media platforms, the information dissemination process is dynamically simulated using a strategy simulation algorithm to evaluate the dissemination effect.

2. The method for identifying and deducing multi-element fusion propagation nodes in online social networks as described in claim 1, characterized in that, The specific steps for evaluating and ranking the importance of nodes in the forwarding network topology based on the centripetal centrality algorithm to obtain the node importance ranking include: Construct an information propagation network, which is represented by an undirected graph, wherein the nodes of the undirected graph are the set of nodes of the forwarding network topology graph, and the edges of the undirected graph are the set of edges of the forwarding network topology graph; The basic topology indicators of each node are calculated based on the core topology parameters within the information propagation network. The core topology parameters include the number of nodes, average degree, and adjacency matrix. The basic topology indicators include degree value, structural hole constraint coefficient, and kernel degree. The set of each node in the information propagation network and the nodes whose shortest path distance is a preset order is denoted as the neighbor set of each node. The shortest path distance is the number of the shortest edges of the connection path in the undirected graph between nodes. Based on the basic topology indicators of each node and the shortest path distance, the centripetal action parameters of each node are dynamically generated. The centripetal action parameters include a mass term, a period term, and a radius term. Based on the neighborhood attenuation coefficient dynamically generated by the shortest path distance and the centripetal effect parameters of each node, the centripetal centrality evaluation index of each node is generated through comprehensive analysis according to the preset self-weight. The nodes are sorted in reverse order according to the centripetal centrality evaluation index, and the result of the reverse sorting is the node importance ranking.

3. The method for identifying and deducing multi-element fusion propagation nodes in online social networks as described in claim 2, characterized in that, In the core topology parameters, the number of nodes is the number of elements contained in the node set, the average degree is the ratio of twice the total number of edges contained in the edge set to the total number of nodes contained in the node set, and the adjacency matrix is ​​a matrix that indicates whether there is a forwarding association relationship between any two nodes in the node set, wherein the rows and columns of the adjacency matrix correspond one-to-one with the nodes in the node set. The rules for selecting the values ​​of the elements in the adjacency matrix are as follows: In the adjacency matrix, if there is a forwarding association between a node in a row and a node in a column, the matrix element at the intersection of the row and the column is 1. If there is no forwarding association between the node corresponding to a row and the node corresponding to a column, then the matrix element at the intersection of the row and the column takes the value of 0.

4. The method for identifying and deducing multi-element fusion propagation nodes in online social networks as described in claim 2, characterized in that, The steps for calculating the basic topology indicators of each node based on the core topology parameters within the information propagation network include: For any node in the node set, obtain all element values ​​of the row where the node is located according to the adjacency matrix, and use the sum of all element values ​​as the degree value of the node. The degree value is used to represent the number of direct connections of the node in the information propagation network. For any node in the node set, the ratio of the direct connection strength between the node and its corresponding neighbor node to the node's degree value is taken as the direct investment ratio of the node to its corresponding neighbor node. The direct investment ratio reflects the proportion of the direct connection strength between the node and its corresponding neighbor node to the total connection strength of the node. Obtain all common neighbor nodes that are connected to both the current node and its corresponding neighbor node. For each common neighbor node, calculate the relationship ratio of the current node to the common neighbor node and the relationship ratio of the common neighbor node to the current neighbor node. The sum of the calculation results for the common neighbor node is taken as the indirect investment ratio of the current node to its neighbor nodes through the common neighbor node. The indirect investment ratio reflects the proportion of the indirect connection strength between the current node and its corresponding neighbor node through the common neighbor node to the total relationship of the node. The connection is a forwarding association relationship. For all neighboring nodes of the node, the direct investment ratio and indirect investment ratio of the node on each neighboring node are summed, and the summation of the squares of the summation results for all neighboring nodes is performed to obtain the structural hole constraint coefficient of the node. The structural hole constraint coefficient is used to represent the degree of structural constraint that the node is subject to in the network. For any node in the node set, the information propagation network is decomposed into kernels. Based on the decomposition results, the kernel level of the node is determined, and the kernel level is used as the kernel degree of the node. The kernel degree is used to represent the global position of the node in the information propagation network.

5. The method for identifying and deducing multi-element fusion propagation nodes in online social networks as described in claim 2, characterized in that, The centripetal centrality evaluation index of each node is obtained as follows: ； In the formula, This represents the centripetal centrality evaluation index of the i-th node. For the weight of the item, For the quality item of the i-th node, Where e is the natural constant, a is the equilibrium coefficient, and a = 10. -n where n is the order of magnitude of the network. The degree value of the i-th node. , This represents the value of the element in the i-th row and j-th column of the adjacency matrix, where i and j are node numbers and i ≠ j, i = 1, 2, 3, ... |V|, j = 1, 2, 3, ... |V|, and |V| is the number of nodes in the core topology parameters. Let be the structural hole constraint coefficient of the i-th node. , This represents the proportion of direct investment made by node i in its neighbor node j. This indicates that node i is connected to its common neighbor nodes. The proportion of indirect input with neighbor node j, ; , This represents the common neighbor of node i and its neighbor node j. This indicates that node i has joined the common neighbor nodes. The proportion of relationships to the total relationships of node i. Represents common neighbor nodes The relationship invested in node j accounts for the node The proportion of total relationships; The m-th order neighborhood attenuation coefficient, m is the order, m=1,2,3. Let d(i,j) be the set of m-order neighbors of the i-th node, where d(i,j) is the shortest path distance and d(i,j) = m, i.e., the periodic term. Let be the kernel degree of the j-th node, i.e., the radius term.

6. The method for identifying and deducing multi-element fusion propagation nodes in online social networks as described in claim 1, characterized in that, The steps of dynamically simulating the information dissemination process based on a strategy simulation algorithm, according to the forwarding of information from popular posts on social media platforms, include: The node whose number of reposts in a popular post on a social media platform exceeds a preset threshold is designated as the first node. Obtain a preset set of probability parameters, which includes the probability of infection and the probability of recovery; The set of the first node and the preset seed nodes is denoted as the initial infection set; Obtain the status of each node, which includes infected, recovered, attacker, and susceptible. A node in the attacker state will not infect other nodes. S1: For nodes in the state of susceptible individuals, dynamically evaluate the infection success probability of each susceptible individual based on the infection probability, and record the nodes that become infected based on the infection success probability as infected individuals. S2: For nodes that are in the state of infected, nodes that become recovered based on the recovery probability will be denoted as recovered nodes; S3: Remove nodes whose status is attacker from the infected set; S4: Remove nodes whose status is attacker from the set of recovered patients; Repeat steps S1-S4 and save the data to the system time stack; Based on the node state at each time step, the expected scale evolution at each time step is dynamically generated; The number of nodes successfully infected by an infection source is counted in real time and recorded as the target number for each infection source. The infection source is a node in the susceptible neighbor set whose state is infected.

7. The method for identifying and deducing multi-element fusion propagation nodes in online social networks as described in claim 6, characterized in that, The method for obtaining the success rate of infection for each susceptible individual is as follows: ； In the formula, This represents the probability of successful infection in the v-th susceptible individual. Let v be the set of neighbors of the vth susceptible person. For the probability of infection, Let be the set of infected individuals at time t, and v be the ID of each susceptible individual, v = 1, 2, 3, ... , Let t be the set of susceptible individuals. , For those recovering at time t, Let u be the set of nodes, where u = 1, 2, 3, ... , Let V be the set of neighbors and infected persons of the v-th susceptible person at time t.

8. The method for identifying and deducing multi-element fusion propagation nodes in online social networks as described in claim 6, characterized in that, The expected size evolution at each time point is obtained as follows: ； In the formula, Let be the number of nodes that are already infected at time t. This represents the probability of a single infected node infecting its neighboring susceptible nodes in a single instance. For recovery rate, , represents the number of infected neighbors of node v at time t. This represents the loss due to external intervention.

9. The method for identifying and deducing multi-element fusion propagation nodes in online social networks as described in claim 6, characterized in that, The method for obtaining the target number of each infection source is as follows: ； In the formula, For the target number of the u-th infection source, Let t be the number of nodes successfully infected by the infection source. For the neighbor set of the uth infected person, To establish the association between the source of infection u and the susceptible individual v, For the source of infection u edge The point at which infection is successful.

10. A system for identifying and extrapolating multi-element fusion propagation nodes in online social networks, applied in the method for identifying and extrapolating multi-element fusion propagation nodes in online social networks as described in any one of claims 1-9, characterized in that, include: Network construction module, importance ranking module, and dynamic simulation module: The network construction module is used to obtain forwarding information of popular posts on social platforms and construct a forwarding network topology based on the forwarding information. In the network topology, nodes are forwarding users and edges are forwarding relationships between corresponding nodes. The importance ranking module is used to evaluate and rank the nodes in the forwarding network topology based on the centripetal centrality algorithm to obtain the node importance ranking. The dynamic simulation module is used to dynamically simulate the information dissemination process based on the forwarding information of popular posts on social platforms and to complete the evaluation of the dissemination effect.

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