Method for identifying key propagation nodes in social network based on improved k-core decomposition

Abstract

The application discloses a kind of key propagation node identification method based on improved k-core decomposition in social network.The application constructs directed weighted graph by obtaining social network topology data and user interaction data;According to network structure and out-degree edge weight, the weighted out-degree of each user node in the current initial network is calculated;The wk-order value of each node is calculated by weighted out-degree;Compare the wk-order value of each node and its out-degree neighbor, find out the core node in the network;According to the centrality of core node, select influential node;Delete core node and its connection, build new initial network;The above process is repeated on the new initial network, and the identification of key propagation node is completed.The method can solve the problems of k-core decomposition algorithm, such as the influence degree between nodes being ignored, the distinction between nodes being not strong, and the coverage range of node influence being easy to overlap, etc., improve the information propagation coverage in social network, and also timely block the spread of public opinion information.

Description

Technical Field

[0001] This invention relates to the field of social network analysis or information dissemination technology, specifically to a method for identifying key propagation nodes in social networks based on improved k-kernel decomposition. Background Technology

[0002] Power networks, transportation networks, trade networks, and social networks all fall under the category of complex networks. Identifying key nodes within these networks has been a crucial task in the field since the inception of complex network research. Influential nodes, in particular, are individual units within a network that exert influence, significantly impacting network connectivity, information dissemination, and innovation diffusion. For example, the disruption of influential nodes in a power network can cause the cascading failure of power plants; influential nodes in a transportation network are transportation hubs; and influential nodes in a social network can greatly facilitate the viral spread of information.

[0003] Social networks, due to their deep integration with daily life, have become one of the most closely watched categories. With the booming development of online social platforms, traditional geographical and kinship ties have been restructured by weak digital connections. Information dissemination has evolved from point-to-point word-of-mouth to explosive, instantaneous spread, with both speed and reach increasing exponentially. This transformation, while giving rise to new business models such as social marketing, targeted information promotion, and public opinion monitoring, has also brought serious challenges such as the viral spread of rumors and group polarization. Superficially, these problems belong to different fields such as commerce, public administration, and information security, but their core technology is highly unified—namely, how to accurately identify influential nodes (key dissemination nodes) in social networks. From a positive perspective, selecting such nodes as information sources can maximize the scope of information dissemination, achieving efficient marketing or policy promotion; from a negative perspective, identifying and suppressing the dissemination behavior of these nodes can effectively block the spread of rumors and maintain the network ecosystem. Therefore, effectively identifying influential nodes in social networks has significant theoretical and practical implications.

[0004] Currently, many methods for identifying influential nodes have been proposed, broadly categorized into two types: greedy algorithms and heuristic algorithms. Greedy algorithms estimate the information propagation range of an influential node set through multiple Monte Carlo simulations, then select the point with the largest marginal influence in each iteration as the influential node for that round. Greedy algorithms can obtain solutions with approximate accuracy but cannot scale to large-scale datasets. Heuristic algorithms focus on finding alternative metrics to approximate the influence propagation range of nodes, thereby reducing the time spent on Monte Carlo simulations. These algorithms have lower time complexity and can scale to large-scale datasets; however, due to the overlapping influence ranges of nodes in the network, their accuracy cannot be guaranteed. Therefore, finding efficient and effective algorithms to identify influential nodes has always been a key research focus for this type of problem.

[0005] In terms of heuristic algorithms, many methods for measuring and ranking node influence have been proposed, such as degree centrality, PageRank, betweenness centrality, and k-kernel decomposition. k-shell, etc. Among these methods, the k-kernel decomposition method can accurately reveal the hierarchical structure of the network from the periphery to the core, identify nodes located in the core position of the network, and has a good effect on identifying the most influential individual nodes. The steps of this method are as follows: starting from k=1, continuously delete nodes with a degree less than or equal to k in the network until there are no nodes with a degree less than or equal to k in the network, and set the k-shell value of the deleted node to k. Then, gradually increase the value of k and repeat the above process until all nodes have been deleted. Figure 1 A specific example is given, in which: The nodes with a k-shell value of 1 are 8 and 9; The nodes with a k-shell value of 2 are 5, 6, 7, 10, and 11. The nodes with a k-shell value of 3 are 1, 2, 3, and 4.

[0006] However, the k-shell decomposition method has the following technical defects when identifying multiple influential nodes in a social network: (1) This method gradually isolates core nodes by node degree, but the influence of a node is not only related to the number of its neighbors, but also to the degree to which it can influence its neighbors. The k-shell decomposition method does not consider the direction and weight of the edges, and cannot identify and utilize this degree of influence between nodes. (2) There are too many nodes in the same level and the distinction between nodes is not strong. For example, nodes 5 and 7 should be more central to the network than nodes 6, 10, and 11, but their k-shell values ​​are all 2. (3) There may be highly connected core groups in the network, resulting in overlapping influence coverage of nodes. For example, the four nodes with the highest k-shell values ​​are closely connected to each other, but only connect with other nodes through node 3. The influence paths of nodes 1, 2, 3, and 4 are almost overlapping. Therefore, this invention proposes a key propagation node identification method based on improved k-shell decomposition in social networks, which reduces the overlap of influence coverage and can more effectively identify influential nodes in the network. Summary of the Invention

[0007] The purpose of this invention is to address the problems of low information dissemination efficiency and lagging public opinion governance caused by inaccurate identification of key nodes in social networks. It provides a method for identifying key propagation nodes in social networks based on an improved k-kernel decomposition. This method acquires social network topology data and user interaction data to construct a directed weighted graph. The weight of each out-degree edge is calculated based on social network behavior parameters such as interaction frequency. According to the network structure and out-degree edge weights, the weighted out-degree of each user node in the initial network is calculated. Building upon traditional k-kernel decomposition, considering edge weights and directions, the wk-order metric is proposed to further refine the node hierarchy. By finding the node with the largest wk-order value compared to its out-degree neighbors, a core node set is obtained, and key propagation nodes are selected accordingly. This method solves problems in k-kernel decomposition algorithms such as neglecting the degree of influence between nodes, weak differentiation between nodes, and easy overlap of node influence coverage. It provides accurate delivery strategies for information push systems, improves the information dissemination coverage in social networks, and can also promptly block the spread of public opinion information.

[0008] A network consists of nodes and the edges connecting them. In a directed weighted graph, the edges between nodes have both direction and weight. If there exists a connection between nodes... i Starting point node j Connecting edges u Then it is called a node. j For nodes i Out-degree neighbors, nodes i For nodes j In-degree neighbors; connected edges u For nodes i Out-degree edge, node j in-degree edge; connecting edge u Weight Represents a node i Able to affect nodes j The degree of.

[0009] The method described in this invention specifically includes the following steps: Step S1: Obtain the topology data and user interaction data of the social network. The topology data includes the follow relationship or friend relationship between user nodes in the social network, and the user interaction data includes the interaction behavior information between users. Step S2: Based on the topology data and user interaction data, construct a directed weighted graph and calculate the weight of each out-degree edge in the social network. The weight of the out-degree edge is determined according to the interaction frequency of the user nodes connected to the edge. Step S3: Based on the network structure and out-degree edge weights, calculate the weighted out-degree of each user node in the current initial network. The weighted out-degree is calculated as follows: for each user node, the sum of the weights of its out-degree edges is taken as the weighted out-degree of that node. Step S4: Based on the weighted out-degree of each user node, the improved k-core decomposition algorithm is used to iteratively calculate the wk-order value of each node. The iterative calculation includes: in each iteration, deleting the user node with the smallest current weighted out-degree and its out-degree edge, and updating the weighted out-degree of the remaining nodes, and taking the iteration number when the node is deleted as the wk-order value of the node. Step S5: Compare the wk-order values ​​of each user node with its out-degree neighbors, and identify the nodes whose wk-order values ​​are not less than the wk-order values ​​of any of its out-degree neighbors and whose wk-order values ​​are greater than a given threshold as core user nodes. Step S6: Select influential nodes from the core user nodes based on the centrality index of the core user nodes in the initial network of this round and the connected branch in the core node sub-network. The centrality index includes degree centrality, weighted degree centrality, and weighted degree-cost ratio. Step S7: Remove the core user nodes and their connections from the initial network of this round. The resulting network is used as the initial network for the next stage. Repeat steps S3 to S6 until the number of selected influential nodes reaches a predetermined threshold or no nodes can be selected, thus obtaining the set of key propagation nodes of the social network. Step S8: Based on the set of key propagation nodes, generate an optimization strategy for the propagation of information on the social network. The optimization strategy is used to instruct the information push system to deliver key information or monitor public opinion for users in the set of key propagation nodes.

[0010] Furthermore, the interactive behavior information includes message forwarding, commenting, and liking.

[0011] Furthermore, the degree centrality, weighted degree centrality, and weighted degree-cost ratio are calculated based on the attention relationship network of user nodes in the social network.

[0012] Furthermore, based on the given social network topology data, the social network is constructed as a directed weighted graph. The wk-order value of each node is calculated by the weighted out-degree of the nodes. The wk-order values ​​of each node and its out-degree neighbors are compared to identify the core nodes in the social network. Based on the centrality of the core nodes, influential nodes are selected. By continuously deleting core nodes and their edges to prevent the problem of overlapping influence, influential nodes are selected multiple times to complete the identification of key propagation nodes.

[0013] Furthermore, the calculation process for the wk-order value of each node in the social network is as follows: Calculate the weighted out-degree of all nodes in the initial network to obtain the minimum weighted out-degree value for this round. Mark the wk-order value of the node whose weighted out-degree is equal to the minimum value as 1. Then delete the node marked with wk-order value 1 and its connected edges in the initial network. Calculate the weighted out-degree of all nodes in the network after deleting the node marked with wk-order value 1 and its connected edges, update the weighted out-degree of the remaining nodes, and mark the wk-order value of the node whose updated weighted out-degree is less than or equal to the minimum value as 2. Delete the marked nodes and their connected edges to obtain a new network, and update the weighted out-degree of the nodes in the network. Repeat the operation multiple times, incrementing the wk-order value of the node marked for each deletion by 1, until there are no nodes in the network with a weighted out-degree less than or equal to the minimum value. After performing a new round of weighted minimum out-degree calculation on the network after the above selection, repeat the above selection and marking operations until there are no nodes in the network with a weighted out-degree less than or equal to the new minimum value. Repeat the weighted minimum out-degree calculation, selection, and marking process multiple times until the wk-order values ​​of all nodes have been marked.

[0014] Furthermore, the identification process of the core user nodes is as follows: Nodes whose wk-order value is not less than the wk-order value of any of their out-degree neighbors and whose wk-order value is greater than a given threshold are identified as core nodes, thus obtaining the core nodes in the social network; core nodes and the edges between core nodes are retained to form a core node subnetwork. There are one or more connected branches in the core node subnetwork. Nodes within the same connected branch are mutually reachable, while nodes between different connected branches are not reachable.

[0015] Furthermore, the selection process for the key propagation node set is as follows: Calculate the centrality of each core point in the initial network of this round, sort the core nodes in descending order of centrality, and sequentially select the core node with the largest centrality and whose connected component has not yet been selected as an influential node, adding it to the key propagation node set, until each connected component has a selected node; if there are core nodes with the same centrality in the same connected component, compare their centralities in the original network and select the node with the higher centrality; if they are still the same, then any one of them can be selected.

[0016] Furthermore, the specific process for calculating the wk-order value is as follows: Step S4.1: Calculate the weighted out-degree of all nodes in the initial network to obtain the minimum weighted out-degree d1 for this round. Mark the wk-order value of the node whose weighted out-degree is equal to the minimum d1 as 1. Then, delete the node marked with wk-order value 1 and its connected edges in the initial network. Calculate the weighted out-degree of all nodes in the network after deleting the node marked with wk-order value 1 and its connected edges, update the weighted out-degree of the remaining nodes, and mark the wk-order value of the node whose updated weighted out-degree is less than or equal to the minimum d1 as 2. Delete the marked nodes and their connected edges to obtain a new network, and update the weighted out-degree of the nodes in the network. Repeat this operation multiple times, incrementing the wk-order value of the selected nodes by 1 each time, until there are no nodes in the network with a weighted out-degree less than or equal to d1. The maximum wk-order value output after the selection is... k The resulting network is G1; Step S4.2: Calculate the weighted out-degree of all nodes in network G1 obtained after the filtering in step S4.1, obtain the minimum value d2 of the new weighted out-degree, and mark the wk-order value of the node whose weighted out-degree is equal to the minimum value d2 as... k +1, then delete the wk-order value marked as k +1 points and the edges connected to them; delete the marked nodes and their edges to obtain a new network, and update the weighted out-degree of the nodes in the network. Repeat the operation multiple times, each time the wk-order value of the marked node is increased by 1 compared to the previous deletion, until there are no nodes in the network with a weighted out-degree less than or equal to d2. Step S4.3: Repeat the method described in step S4.2 multiple times to perform the selection and marking until the wk-order values ​​of all nodes have been marked.

[0017] To implement the above method, the present invention also proposes an electronic device, including a processor and a memory, wherein the memory stores a computer program, and the processor executes the computer program to implement the key propagation node identification method based on improved k-core decomposition in the social network. Attached Figure Description

[0018] Figure 1 Example diagram of the k-core decomposition method; Figure 2 This is a schematic diagram illustrating the calculation process of the wk-order value of each node in the embodiment; Figure 3 This is a schematic diagram of the core node sub-network constructed in step S5 of the embodiment; Figure 4 This is a schematic diagram of the new initial network in step S7 of the embodiment; Figure 5This is a graph showing the results of selecting the top 5 most influential nodes using the method described in this invention in an embodiment. Figure 6 The graph shows the results of selecting the top 5 nodes by influence using the k-core decomposition method. Detailed Implementation

[0019] The present invention will be further described below with reference to the accompanying drawings.

[0020] This invention provides an electronic device, specifically, the electronic device includes a memory and a processor. The memory is used to store a program, and the processor executes the program after receiving an execution instruction. The method executed in this invention can be applied to the processor or implemented by the processor.

[0021] A method for identifying key propagation nodes in social networks based on improved k-kernel decomposition includes the following steps: Step S1: Obtain the topology data and user interaction (forwarding, commenting, and favoriting) data of the social network. This data can be obtained through web crawling and other technologies. This example assumes there are 11 users in the social network. The topology data and interaction data between users are as follows, where the numbers in parentheses represent the interaction frequency. For example, User 1: Following User 2 (0.2) means that the frequency with which User 1 forwards, comments on, and favorites the information posted by User 2 is 0.2. User 1: Follows User 2 (0.2), 3 (0.4), 4 (0.3) User 2: Follows User 1 (0.3), 3 (0.4), 4 (0.2) User 3: Follows User 1 (0.2), 2 (0.3), 4 (0.2), 5 (0.1) User 4: Follows User 1 (0.3), 2 (0.2), 3 (0.3) User 5: Follows users 3 (0.3), 6 (0.2), 7 (0.3), 8 (0.2) User 6: Follows users 5 (0.4), 7 (0.3), and 9 (0.2) User 7: Follows users 5 (0.3), 6 (0.2), 10 (0.1), 11 (0.1) User 8: Following User 5 (0.6) User 9: Following User 6 (0.5) User 10: Follows User 7 (0.6), 11 (0) User 11: Follows User 7 (0.5), 10 (0.1) Step S2: Based on the topology data and user interaction data, define users as nodes, and then... u Follow users vDefined as a line from user v Pointing to user u The directed edges ( v , u The weight of the edge is the user. v The information posted was by users u The frequency of forwarding, commenting, and saving is used to construct a directed weighted graph, such as... Figure 2 As shown in (1); Step S3: Based on the network structure and out-degree edge weights, calculate the weighted out-degree of each user node in the current initial network. The weighted out-degree is calculated as follows: For each user node, the sum of the weights of its out-degree edges is taken as the weighted out-degree of that node. For example, the out-degree edges of user 1 are (1, 2), (1, 3), and (1, 4), with weights of 0.3, 0.2, and 0.3 respectively. Then, the weighted out-degree of user 1 is 0.3 + 0.2 + 0.3 = 0.8.

[0022] Step S4: Calculation of wk-order value for each node: In this embodiment, the initial network structure and edge weights are as follows: Figure 2 As shown in (1): Round 1: Traverse the initial network G (1) For all nodes in the initial network, calculate the value of each node in turn. i Weighted out-degree wd i , ,in For nodes i The set of all out-degree neighbors. Obtain the minimum weighted out-degree d1 in this round, mark the wk-order value of the node whose weighted out-degree equals the minimum d1 as 1, and then in the initial network G... (1) Delete the nodes marked with a wk-order value of 1 and the edges connected to them, and label the network as G. (2) ; In this embodiment, the initial weighted minimum out-degree is d1=0.1. The wk-order value of node 11 is set to 1, and node 11 and its connected edges are deleted (e.g., ...). Figure 2 (as shown in (2)).

[0023] Then recalculate the remaining nodes in the new network G. (2) In the weighted out-degree algorithm, after the update, the weighted out-degree of node 10 is less than or equal to 0.1, so its wk-order value is set to 2, and node 10 and its connected edges are deleted (e.g., ...). Figure 2 (as shown in (3)). Recalculate the remaining nodes in the new network G (3) The weighted out-degrees are calculated, and the minimum weighted out-degree is 0.2, which is greater than d1. The next round of selection is then initiated.

[0024] Second round: Network G updated after the first round (3) The nodes with the minimum weighted out-degree d2 = 0.2 are nodes 8 and 9. Set the wk-order value of nodes 8 and 9 to 3, and delete nodes 8 and 9 and their connecting edges (e.g., ...). Figure 2 (as shown in (4)).

[0025] Then recalculate the remaining nodes in the new network G. (4) The weighted out-degree is calculated, and at this point there are no nodes in the network with a weighted out-degree less than or equal to d2, so the next round of selection begins.

[0026] Third round: Network G after the second round of updates (4) The node with the minimum weighted out-degree d3 = 0.4 is node 6. Set the wk-order value of node 6 to 4, and delete node 6 and its connected edges (e.g., ...). Figure 2 (as shown in (5)).

[0027] Then recalculate the remaining nodes in the new network G. (5) The weighted out-degrees of nodes 5 and 7 are calculated, and their weighted out-degrees (0.4 and 0.3 respectively) are both less than or equal to d3. The wk-order values ​​of nodes 5 and 7 are set to 5, and nodes 5 and 7, along with their connecting edges, are deleted. Figure 2 As shown in (6)).

[0028] Then recalculate the remaining nodes in the new network G. (6) The weighted out-degree is calculated, and at this point there are no nodes in the network with a weighted out-degree less than or equal to d3, so the next round of selection begins.

[0029] Fourth round: Network G after the third round of updates (6) The nodes with the minimum weighted out-degree d4 = 0.7 are node 2 and node 4 (e.g., ...). Figure 2 As shown in (7), set the wk-order value of nodes 2 and 4 to 6, and delete nodes 2 and 4 and their connecting edges (as shown in Figure 7). Figure 2 (as shown in (8)).

[0030] Then recalculate the remaining nodes in the new network G. (7) In the weighted out-degree calculation, the weighted out-degrees of nodes 1 and 3 (0.2 and 0.4 respectively) are both less than d4. The wk-order values ​​of nodes 1 and 3 are set to 7, and these two nodes are deleted (e.g., ...). Figure 2 (as shown in (9)).

[0031] At this point, the wk-order values ​​for all nodes have been calculated, and the wk-order values ​​for all nodes are as follows: Figure 2As shown in (10).

[0032] Step S5: Construct core nodes and their sub-networks: Define nodes whose wk-order value is not less than the wk-order value of any of their out-degree neighbors, and whose wk-order value is greater than a given threshold φ (assuming φ=1 in this example) as core nodes. Accordingly, the core nodes in this embodiment are: 1, 3, and 7.

[0033] Retain the core nodes 1, 3, and 7 and the edges connecting them, forming a structure like... Figure 3 The core node subnetwork shown in this embodiment has two connected branches.

[0034] Step S6: Select Influential Nodes. Based on the real-world scenario, select appropriate metrics (such as degree, weighted out-degree, weighted out-degree / cost ratio, etc.) to calculate the centrality of each core user node in the initial network of this round.

[0035] In this embodiment, the centrality of each core point is calculated by weighted out-degree, and the core nodes are sorted from largest to smallest centrality as 7 (weighted out-degree is 1.7), 3 (weighted out-degree is 1.4), and 1 (weighted out-degree is 0.8).

[0036] Select node 7 as the first influence node and node 3 as the second influence node. With one node selected in each of the two connected branches, the influence node selection process ends.

[0037] Step S7, as follows Figure 4 As shown, the network in which all core nodes (i.e., nodes 1, 3, and 7) in step S5 are deleted is used as the initial network, and the operations of steps S3 to S6 are repeated.

[0038] In this embodiment, steps S3-S4 are repeated to obtain the wk-order value of each node in the network: wk-order=1: Nodes 10 and 11.

[0039] wk-order=2: Nodes 2, 4, 9, 8.

[0040] wk-order=3:node6.

[0041] wk-order=4:node5.

[0042] Repeat step S5 to select the core nodes as node 5, node 2, node 4, node 10, and node 11.

[0043] Repeat step S6 and select nodes 5, 2, and 10 as influence nodes.

[0044] At this point, the top 5 most influential nodes in this embodiment have been selected, namely node 7, node 3, node 5, node 2, and node 10. The selection results are as follows: Figure 5 As shown.

[0045] Step S8: Based on the set of key propagation nodes, generate an optimized strategy for social network information propagation. That is, in the context of social marketing, select nodes 7, 3, 5, 2, and 10 for marketing information promotion; in the context of public opinion monitoring, focus on monitoring nodes 7, 3, 5, 2, and 10 to promptly block the spread of public opinion information.

[0046] To demonstrate the effectiveness of the method described in this invention, the k-kernel decomposition method was used to select influential nodes on the same network. The selection results are as follows: Figure 6 As shown; comparison Figure 5 and Figure 6 It can be seen that the influential nodes obtained by the k-core decomposition method exhibit significant clustering, weak node distinguishability, and large overlap in the influence coverage of nodes. Furthermore, the top 5 influential nodes cannot directly influence nodes 9, 10, and 11, making these nodes even more difficult to influence. The method proposed in this invention can obtain influential nodes in a distributed manner, with high distinguishability between them, reducing the overlap in influence coverage. Moreover, all nodes in the network are within the set of out-degree neighbors of the top 5 influential nodes, ensuring effective influence propagation.

[0047] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for identifying key propagation nodes in social networks based on improved k-kernel decomposition, characterized in that, Specifically, the following steps are included: Step S1: Obtain the topology data and user interaction data of the social network. The topology data includes the follow relationship or friend relationship between user nodes in the social network, and the user interaction data includes the interaction behavior information between users. Step S2: Based on the topology data and user interaction data, construct a directed weighted graph and calculate the weight of each out-degree edge in the social network. The weight of the out-degree edge is determined according to the interaction frequency of the user nodes connected to the edge. Step S3: Based on the network structure and out-degree edge weights, calculate the weighted out-degree of each user node in the current initial network. The weighted out-degree is calculated as follows: for each user node, the sum of the weights of its out-degree edges is taken as the weighted out-degree of that node. Step S4: Based on the weighted out-degree of each user node, the improved k-core decomposition algorithm is used to iteratively calculate the wk-order value of each node. The iterative calculation includes: in each iteration, deleting the user node with the smallest current weighted out-degree and its out-degree edge, and updating the weighted out-degree of the remaining nodes, and taking the iteration number when the node is deleted as the wk-order value of the node. Step S5: Compare the wk-order values ​​of each user node with its out-degree neighbors, and identify the nodes whose wk-order values ​​are not less than the wk-order values ​​of any of its out-degree neighbors and whose wk-order values ​​are greater than a given threshold as core user nodes. Step S6: Select influential nodes from the core user nodes based on the centrality index of the core user nodes in the initial network of this round and the connected branch in the core node sub-network. The centrality index includes degree centrality, weighted degree centrality, and weighted degree-cost ratio. Step S7: Remove the core user nodes and their connections from the initial network of this round. The resulting network is used as the initial network for the next stage. Repeat steps S3 to S6 until the number of selected influential nodes reaches a predetermined threshold or no nodes can be selected, thus obtaining the set of key propagation nodes of the social network. Step S8: Based on the set of key propagation nodes, generate an optimization strategy for the propagation of information on the social network. The optimization strategy is used to instruct the information push system to deliver key information or monitor public opinion for users in the set of key propagation nodes.

2. The method for identifying key propagation nodes in social networks based on improved k-kernel decomposition as described in claim 1, characterized in that, The interactive behavior information includes message forwarding, commenting, and liking.

3. The method for identifying key propagation nodes in social networks based on improved k-kernel decomposition as described in claim 1, characterized in that, The degree centrality, weighted degree centrality, and weighted degree-cost ratio are calculated based on the attention relationship network of user nodes in the social network.

4. The method for identifying key propagation nodes in social networks based on improved k-kernel decomposition as described in claim 1, characterized in that, Based on the given social network topology data, the social network is constructed as a directed weighted graph. The wk-order value of each node is calculated by the weighted out-degree of the nodes. The wk-order values ​​of each node and its out-degree neighbors are compared to identify the core nodes in the social network. Based on the centrality of the core nodes, influential nodes are selected. To prevent the problem of overlapping influence, core nodes and their edges are continuously deleted. Influential nodes are selected multiple times to complete the identification of key propagation nodes.

5. The method for identifying key propagation nodes in social networks based on improved k-kernel decomposition as described in claim 1, characterized in that, The calculation process for the wk-order value of each node in a social network is as follows: Calculate the weighted out-degree of all nodes in the initial network to obtain the minimum weighted out-degree value for this round. Mark the wk-order value of the node whose weighted out-degree is equal to the minimum value as 1. Then delete the node marked with wk-order value 1 and its connected edges in the initial network. Calculate the weighted out-degree of all nodes in the network after deleting the node marked with wk-order value 1 and its connected edges, update the weighted out-degree of the remaining nodes, and mark the wk-order value of the node whose updated weighted out-degree is less than or equal to the minimum value as 2. Delete the marked nodes and their connected edges to obtain a new network, and update the weighted out-degree of the nodes in the network. Repeat the operation multiple times, incrementing the wk-order value of the node marked for each deletion by 1, until there are no nodes in the network with a weighted out-degree less than or equal to the minimum value. After performing a new round of weighted minimum out-degree calculation on the network after the above selection, repeat the above selection and marking operations until there are no nodes in the network with a weighted out-degree less than or equal to the new minimum value. Repeat the weighted minimum out-degree calculation, selection, and marking process multiple times until the wk-order values ​​of all nodes have been marked.

6. The method for identifying key propagation nodes in social networks based on improved k-kernel decomposition as described in claim 1, characterized in that, The identification process of the core user nodes is as follows: Nodes whose wk-order value is not less than the wk-order value of any of their out-degree neighbors and whose wk-order value is greater than a given threshold are identified as core nodes, thus obtaining the core nodes in the social network; core nodes and the edges between them are retained to form a core node subnetwork. There are one or more connected branches in the core node subnetwork. Nodes within the same connected branch are mutually reachable, while nodes between different connected branches are not reachable.

7. The method for identifying key propagation nodes in social networks based on improved k-kernel decomposition as described in claim 1, characterized in that, The selection process for the key propagation node set is as follows: Calculate the centrality of each core point in the initial network of this round, sort the core nodes in descending order of centrality, and sequentially select the core node with the largest centrality and whose connected component has not yet been selected as an influential node, adding it to the key propagation node set, until each connected component has a selected node; if there are core nodes with the same centrality in the same connected component, compare their centralities in the original network and select the node with the higher centrality; if they are still the same, then any one of them can be selected.

8. The method for identifying key propagation nodes in a social network based on improved k-kernel decomposition as described in claim 5, characterized in that, The specific process for calculating the wk-order value is as follows: Step S4.1: Calculate the weighted out-degree of all nodes in the initial network to obtain the minimum weighted out-degree d1 in this round. Mark the wk-order value of the node whose weighted out-degree is equal to the minimum value d1 as 1. Then delete the node marked with wk-order value 1 and the edge connected to it in the initial network. Calculate the weighted out-degree of all nodes in the network after deleting the node marked with wk-order value 1 and the edge connected to it, update the weighted out-degree of the remaining nodes, and mark the wk-order value of the node whose updated weighted out-degree is less than or equal to the minimum value d1 as 2. Delete the marked nodes and their connected edges to obtain a new network, and update the weighted out-degree of the nodes in the network. Repeat the operation multiple times, increasing the wk-order value of the node marked each time by 1, until there are no nodes in the network with a weighted out-degree less than or equal to d1. The maximum wk-order value output after filtering is k The resulting network is G1; Step S4.2: Calculate the weighted out-degree of all nodes in network G1 obtained after the filtering in step S4.1, obtain the minimum value d2 of the new weighted out-degree, and mark the wk-order value of the node whose weighted out-degree is equal to the minimum value d2 as... k +1, then delete the wk-order value marked as k +1 points and the edges connected to them; delete the marked nodes and their edges to obtain a new network, and update the weighted out-degree of the nodes in the network. Repeat the operation multiple times, each time the wk-order value of the marked node is increased by 1 compared to the previous deletion, until there are no nodes in the network with a weighted out-degree less than or equal to d2. Step S4.3: Repeat the method described in step S4.2 multiple times to perform the selection and marking until the wk-order values ​​of all nodes have been marked.

9. An electronic device comprising a processor and a memory, the memory storing a computer program, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1-8.

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