Method for identifying influential nodes in complex networks based on neighbor nodes and information interaction

Abstract

The application relates to the technical field of complex networks, and discloses a complex network influence node identification method based on neighbor nodes and information interaction, which comprises the following steps: constructing an undirected and weightless complex network based on real data and generating an adjacency matrix; calculating a network propagation threshold and the number of information interaction paths of a node pair under different path lengths, and then obtaining an information interaction probability matrix between the node pair; determining a neighbor diversity index based on neighbor information of the node, and calculating inherent influence of the node in combination with a node degree value; combining the inherent influence with the information interaction probability matrix to calculate comprehensive influence of the node; and sorting the network nodes according to the comprehensive influence to identify the nodes with key influence. The application introduces a neighbor diversity index and a multi-path interaction probability mechanism, overcomes the limitations of traditional methods which only consider the shortest path interaction and have low distinguishability, and can more accurately identify key nodes in a complex network.

Description

Technical Field

[0001] This invention belongs to the field of complex network technology, specifically relating to a method for identifying influential nodes in complex networks based on neighbor nodes and information interaction. Background Technology

[0002] Although existing research has developed a rich set of indicators for identifying influential nodes, such as degree centrality, betweenness centrality, proximity centrality, and K-shell, traditional centrality methods still have several limitations. Methods based on local topological features, such as degree centrality, are computationally efficient, but their accuracy is limited because they ignore global network structure information, making it difficult to distinguish nodes in different locations with similar local features. Methods based on global paths, such as betweenness centrality and proximity centrality, have high accuracy, but their computational complexity is usually high, facing scalability bottlenecks in large-scale complex networks and failing to meet the real-time processing needs of massive amounts of data. Furthermore, most traditional methods rely on static network assumptions; for example, the K-shell method describes node influence through topological hierarchies, but it cannot reflect the time-varying structures and dynamic interaction processes prevalent in real systems. Within this framework, the identification of node influence often relies solely on the network structure itself, ignoring the moderating role of specific propagation dynamics mechanisms, resulting in insufficient applicability and generalization ability in different propagation environments. The above methods identify influential nodes from different perspectives, but each has its own limitations, such as (1) methods based on local information tend to overlook the role of some seemingly unimportant but actually important nodes in the network, thereby reducing the accuracy of identification; (2) methods based on global information have high computational complexity and are often not suitable for large-scale networks; (3) most methods are not suitable for dynamically changing networks.

[0003] In addition to the problems mentioned above, existing technologies, when identifying influential nodes in complex networks, often only consider the unidirectional propagation of information from lower-order nodes to higher-order nodes along the shortest path, neglecting the possibility of information interacting from higher-order nodes to lower-order nodes via non-shortest paths. Secondly, they do not fully consider the impact of the differences in the influence of nodes themselves on the magnitude of influence transmission, which means that different nodes transmit the same influence under the same interaction probability. These factors lead to limited accuracy in the identification of existing methods. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for identifying influential nodes in complex networks based on neighbor nodes and information interaction, so as to realize the identification of the propagation influence of nodes based on a comprehensive identification mechanism of neighbor diversity index and information interaction probability.

[0005] To address the aforementioned technical problems, this invention provides a method for identifying influential nodes in complex networks based on neighbor nodes and information interaction, the specific process of which is as follows:

[0006] Step S1: Construct an undirected, unweighted complex network based on the network topology data and generate an adjacency matrix;

[0007] Step S2: Calculate the propagation threshold of the network and the matrix of the number of information interaction paths between node pairs under different path lengths. Then, based on the calculation of the information interaction probability of node pairs under different path lengths, obtain the information interaction probability matrix M between node pairs.

[0008] Step S3: Based on the node's neighbor information, determine the node's neighbor diversity index, and combine the neighbor diversity index with the node's degree value to calculate the node's inherent influence. ;

[0009] Step S4: Combine the inherent influence of the nodes With the information interaction probability matrix M, the comprehensive influence of computing nodes ;

[0010] Step S5: Based on overall influence The nodes in the network are sorted to identify those with critical influence.

[0011] As an improvement to the present invention's method for identifying influential nodes in complex networks based on neighbor nodes and information interaction:

[0012] The propagation threshold is calculated based on the network's first-order average degree and second-order average degree:

[0013]

[0014] in, Indicates the first-order average degree. , This represents the number of edges in the network. Indicates the number of nodes in the network; It represents the second-order average degree.

[0015] As a further improvement to the method for identifying influential nodes in complex networks based on neighbor nodes and information interaction of the present invention:

[0016] The information interaction path number matrix includes the path number matrix where the path length between node pairs is 1. A matrix of the number of paths with a path length of 2 And a path count matrix with a path length of 3. :

[0017]

[0018]

[0019]

[0020] in, Represents the adjacency matrix. Represents a node The degree value, Represents a node The set of neighboring nodes.

[0021] As a further improvement to the method for identifying influential nodes in complex networks based on neighbor nodes and information interaction of the present invention:

[0022] The method for calculating the probability of information interaction between nodes under different path lengths is as follows:

[0023]

[0024] in, Represents a node and At a distance of The probability of information interaction under the path, The distance between the two nodes is The number of paths.

[0025] As a further improvement to the method for identifying influential nodes in complex networks based on neighbor nodes and information interaction of the present invention:

[0026] The probability matrix M of information interaction between node pairs is calculated as follows:

[0027] .

[0028] As a further improvement to the method for identifying influential nodes in complex networks based on neighbor nodes and information interaction of the present invention:

[0029] The method for calculating the neighbor diversity is as follows:

[0030]

[0031] in, Represents a node The value of neighborhood diversity, Represents a node The degree value, Represents a node The ranking of neighbor diversity values ​​in descending order. express Nodes in , Represents the set of nodes in the network. Represents a node The neighborhood group, Represents a node The set of neighbors.

[0032] As a further improvement to the method for identifying influential nodes in complex networks based on neighbor nodes and information interaction of the present invention:

[0033] The method for calculating the inherent influence is as follows:

[0034] .

[0035] As a further improvement to the method for identifying influential nodes in complex networks based on neighbor nodes and information interaction of the present invention:

[0036] The method for calculating the overall influence is as follows:

[0037]

[0038] in, Information interaction probability matrix The elements in It is the set of nodes in the network.

[0039] In summary, this invention can effectively assess and rank the influence of nodes in complex networks, thereby accurately identifying key influential nodes. Compared with existing technologies, the beneficial effects of this invention are mainly reflected in the following three aspects:

[0040] (1) A comprehensive identification mechanism that integrates the characteristics of node neighbors and the probability of information interaction is proposed, which can more effectively identify influential nodes in complex networks.

[0041] (2) The introduction of the "neighbor diversity" index, combined with the node degree value, effectively distinguishes the differences in the inherent influence of different nodes and overcomes the limitation that node influence is treated equally under the same interaction probability.

[0042] (3) By introducing propagation dynamics theory, three effective information interaction methods between node pairs are proposed, breaking through the assumption of traditional methods that only consider the shortest path interaction, and providing corresponding methods for calculating the probability of information interaction, making the characterization of interaction probability more realistic and effective. Through the above innovations, this invention achieves an accurate description of the communication probability between nodes and precise identification of influential nodes. The proposed general identification method can be directly applied to specific technical problems in multiple fields such as power network structure optimization, aviation hub layout planning, and precise guidance of social information flow.

[0043] In summary, this invention addresses the bias in calculating information interaction probability caused by the traditional method's assumption that information propagates only along the shortest path. It proposes a more effective interaction probability evaluation mechanism while maintaining computational efficiency. It also overcomes the problem that existing methods do not distinguish the influence of different nodes under the same interaction probability, and achieves differentiated identification of the influence of node propagation. Attached Figure Description

[0044] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0045] Figure 1 A flowchart illustrating a method for identifying influential nodes in complex networks based on neighbor nodes and information interaction;

[0046] Figure 2 An example diagram of the undirected and unweighted complex network constructed in this invention;

[0047] Figure 3 This is a comparison chart of the Jaccard coefficients of this invention and 10 common algorithms under EEC network conditions;

[0048] Figure 4 This is a comparison chart of the Jaccard coefficients of this invention and 10 common algorithms in an email network environment.

[0049] Figure 5 The graph shows a comparison of the Jaccard coefficients of this invention with 10 common algorithms under the Erdos network.

[0050] Figure 6 The graph shows a comparison of the Jaccard coefficients of this invention with 10 common algorithms under the GrQc network.

[0051] Figure 7 This is a comparison chart of the Jaccard coefficients of the present invention and 10 common algorithms under the Hamster network;

[0052] Figure 8 This is a comparison chart of the Jaccard coefficients of this invention and 10 common algorithms under the Jazz network;

[0053] Figure 9 The graph shows a comparison of the Jaccard coefficients of this invention with 10 common algorithms under the NS network.

[0054] Figure 10 The graph shows a comparison of the Jaccard coefficients of this invention with 10 common algorithms under a PB network.

[0055] Figure 11 This is a comparison chart of the Jaccard coefficients of this invention and 10 common algorithms under the USAir network;

[0056] Figure 12 A comparison of the imprecise functions of this invention with 10 common algorithms under an EEC network;

[0057] Figure 13 A comparison chart of the imprecise functions of this invention and 10 common algorithms in an email network environment;

[0058] Figure 14 A comparison of the imprecise functions of this invention with 10 common algorithms under an Erdos network;

[0059] Figure 15 A comparison of the imprecise functions of this invention with 10 common algorithms under the GrQc network;

[0060] Figure 16 A comparison of the imprecise functions of this invention with 10 common algorithms under the Hamster network;

[0061] Figure 17 A comparison of the imprecise functions of this invention with 10 common algorithms under the Jazz network;

[0062] Figure 18 A comparison of the imprecise functions of this invention with 10 common algorithms under the NS network;

[0063] Figure 19 A comparison of the imprecise functions of this invention with 10 common algorithms under a PB network;

[0064] Figure 20 This is a comparison chart of the imprecise functions of the present invention and 10 common algorithms under the USAir network. Detailed Implementation

[0065] The present invention will be further described below with reference to specific embodiments, but the scope of protection of the present invention is not limited thereto:

[0066] Example 1: A method for identifying influential nodes in complex networks based on neighbor nodes and information interaction, such as... Figures 1-2 As shown, specifically:

[0067] Step 1: Construct an undirected, unweighted complex network and its adjacency matrix

[0068] Based on data from real-world example networks, the relationships between nodes and edges are extracted to obtain topological data for real-world networks such as power networks, transportation networks, or social networks. The obtained data is then input into a computer to construct a network containing... Each node The structure diagram of an undirected, unweighted complex network with a single edge. Assume the undirected, unweighted complex network to be processed is... ,in For the set of nodes in the network, Let be the set of edges in the network. Based on the constructed network structure graph, generate a network adjacency matrix that is easy for computer processing. , where nodes and nodes If there is an edge between them Otherwise .for Figure 2 The constructed undirected, unweighted complex network has 8 nodes and 8 edges. The neighbor information of the nodes is as follows: , , , , , , and ,in, This indicates that the neighbors of node 1 are nodes 2, 3, 4, and 5. Figure 2 The adjacency matrix of the undirected, unweighted complex network shown is As shown below:

[0069] (1)

[0070] In specific application scenarios, the undirected and unweighted complex network model of this invention has a clear mapping relationship with the entities of the instance network in the real-world scenario. Specifically, (1) In the power network scenario, the network nodes correspond to the physical facilities in the power system, such as power plants, substations, distribution stations, or important load centers; the network edges correspond to the transmission lines or power tie lines connecting these physical facilities. The influence of a node directly reflects the criticality of the power facility in power grid power flow distribution, system stability, and resilience. (2) In the aviation network scenario, the network nodes correspond to each airport or airport city; the network edges correspond to the direct flight routes between two airports. The influence of a node characterizes the hub status of the airport in the connectivity of the route network, passenger transfer efficiency, and the robustness of the entire air transport system. (3) In the social network scenario, the network nodes correspond to user accounts or information publishing entities on the social platform; the network edges correspond to the "following," "friend" relationships, or stable information interaction paths formed between users. The influence of a node measures the user's ability to act as a key hub or source of dissemination in information dissemination, opinion diffusion, or community structure.

[0071] Step 2: Calculate the probability of information exchange between node pairs.

[0072] First, based on the propagation dynamics model, the network propagation threshold is used to represent the probability of information interaction between adjacent nodes. Building upon this, to overcome the limitation of information only propagating unidirectionally from lower-order nodes to higher-order nodes, this invention proposes three effective information interaction methods to cover the scenario of information propagating from higher-order nodes to lower-order nodes: (1) two nodes interact along a path of length 1; (2) two nodes interact along a path of length 2; and (3) two nodes interact along a path of length 3. This invention limits the information interaction distance to within 3. Given that the interaction probability is low and the computational cost is high beyond this distance, its contribution to the result is negligible. All interaction paths are summarized to calculate the final information interaction probability between node pairs.

[0073] (1) Calculate the propagation threshold of the network The calculation formula is as follows:

[0074] (2)

[0075] in, The first-order average degree is represented by the following formula for undirected and unweighted complex networks: , This represents the number of edges in the network. Indicates the number of nodes in the network; This represents the second-order average degree. For Figure 2 To put it another way: .

[0076] (2) Calculate the path length as ( The matrix of the number of information exchange paths between nodes is given by the following formula:

[0077] (3)

[0078] (4)

[0079] (5)

[0080] in, Represents the adjacency matrix. , and The elements in the text represent nodes. and The matrix contains the number of paths with distances of 1, 2, and 3 between nodes, where each element represents a path with a distance of 1, 2, and 3 between nodes. The number of paths, Represents a node The degree value, Represents a node The set of neighboring nodes.

[0081] Figure 2 The matrix shown represents the number of information exchange paths between node pairs in an undirected, unweighted complex network. , , They are respectively:

[0082] (6)

[0083] (7)

[0084] (8)

[0085] (3) Determine the information interaction probability of nodes under different information interaction paths

[0086] The probability of information exchange between nodes depends on the cumulative effect of the exchange probabilities between adjacent nodes along their connection path. For a node... and Given path length The probability of information interaction is calculated using the following formula:

[0087] (9)

[0088] in, Represents a node and At a distance of The probability of information interaction under the path, The threshold for network propagation. The distance between the two nodes is The number of paths corresponds to the information interaction path number matrix calculated in step two. , , The elements in.

[0089] (4) Calculate the probability of effective information exchange between node pairs.

[0090] Combining the three interaction methods, the information exchange probability matrix between node pairs is calculated by the following formula:

[0091] (10)

[0092] Figure 2 The information interaction probability matrix of the undirected and unweighted complex network shown is for:

[0093] (11).

[0094] Step 3: Integrate the influence of neighboring nodes to determine the inherent influence of a node.

[0095] To effectively distinguish the inherent influence differences among different nodes, this invention proposes an index called "neighbor diversity," which is combined with node degree value to jointly characterize the inherent influence of a node. Neighbor diversity considers the influence of other nodes on the target node from a global perspective, effectively reflecting the differences between nodes. The number of neighbors of a node is its node degree value, which, as a supplement to local topological features, compensates for the inadequacy of neighbor diversity in distinguishing unimportant nodes. By integrating the two, this invention can accurately characterize the inherent influence of a node, thus solving the problem of decreased distinction accuracy caused by different nodes transmitting the same influence under the same information interaction probability. The specific calculation process of the inherent influence of a node is as follows:

[0096] (1) Determine the neighbor diversity index of a node based on its neighbor information. The formula for calculating neighbor diversity is as follows:

[0097] (12)

[0098] in, Represents a node The value of neighborhood diversity, Represents a node The degree value, Represents a node The ranking of neighbor diversity values ​​in descending order. express Nodes in , Represents the set of nodes in the network. Represents a node The neighborhood group, Represents a node The set of neighbors.

[0099] It is worth noting that the calculation of neighbor diversity is an iterative process that needs to be performed according to... Size from 1 to The calculation must be performed step-by-step, not skipping steps. For example, in a network with n=100 nodes, the neighbor diversity of node 10 cannot be calculated directly. Instead, the neighbor diversity of the node with the largest neighbor diversity value must be calculated first, and then the neighbor diversity value of each subsequent node must be determined step-by-step. This design has the following advantages:

[0100] (1) The calculation of the neighbor diversity of a node needs to take into account the influence of other nodes on it. This describes the influence of a node from a global perspective. The node's influence represented by the global perspective is more in line with its true influence.

[0101] (2) To influence other nodes in the network with the minimum number of nodes and the maximum scope. For example, if 10 nodes need to be selected, selecting 10 nodes according to the neighbor diversity index can maximize the number of their different neighbors, while other indicators may not. Applying the neighbor diversity index to the real world has a great advantage. For example, for a power network, due to objective factors such as manpower, financial resources, and material resources, only 10 key node facilities such as transmission piles and substations can be protected. Obviously, selecting key nodes that can maximize the impact on other node facilities as the protection targets means that when problems occur in the power network, as long as these key facilities are not damaged, the impact will always be relatively small.

[0102] This represents a node. The neighbor diversity value, and it is a whole, composed of and It consists of two parts. Among them, Corresponding unique node Because in calculating the current node When calculating the neighbor diversity value, it is necessary to consider the neighbor information of nodes that have already been calculated, and through... This method can record previous ( There are ) nodes. Then, the calculation to be performed at this point... Nodes are The neighbor diversity value of a node can then be represented by the formula (12) mentioned in the paper. This complex design is mainly due to the fact that the neighbor diversity value is calculated step by step through an iterative loop.

[0103] for Figure 2 To be honest Here, 4, 2, 3, 1, 2, 1, 2, and 1 represent the degree values ​​of nodes 1-8, respectively. This also shows that... This corresponds to node 1. The neighbor diversity values ​​of the other nodes can be obtained sequentially according to the proposed calculation formula.

[0104] (2) The formula for calculating the inherent influence of a node is as follows:

[0105] (13)

[0106] in, The numerical value represents the node Neighbor diversity value, Represents a node The degree value.

[0107] Step 4: Calculate the node's overall influence based on its inherent influence and the information interaction probability between node pairs. Specifically, if a node can reach a target node through an information interaction path, then that node can inherit a portion of the target node's influence, with the inheritance weight determined by the information interaction probability between the two. After obtaining the inherent influence of all relevant nodes and the information interaction probability between node pairs, the node's overall influence value can be calculated. The node's overall influence is calculated using the following formula:

[0108] (14)

[0109] in, Represents a node The inherent influence, Information interaction probability matrix The elements in the text represent nodes. and The probability of information exchange between them.

[0110] Step 5: Based on overall influence The nodes in the network are sorted to identify those with critical influence.

[0111] By quantifying and ranking the influence of nodes, the importance ranking of each node in the network can be obtained. Based on this, mapping the ranking results to physical facilities in the real system allows for the precise identification of entities that have a critical impact on system functionality. Figure 2 Taking the network shown as an example, after identifying key power plants, substations, and load centers, the physical protection and operational monitoring of these facilities can be strengthened in a targeted manner. When the power grid encounters natural disasters, human-caused damage, or sudden failures, prioritizing the protection of key facilities can effectively limit the scope of fault propagation, significantly improve the resilience and power supply reliability of the power grid, thereby avoiding large-scale power outages and ensuring the normal operation of social and economic activities and public safety.

[0112] Experimental verification:

[0113] This experiment aims to evaluate the effectiveness of the proposed method for identifying influential nodes. To this end, the method of this invention (hereinafter referred to as the PPCN algorithm) is compared with 10 common algorithms on 9 real networks. The evaluation metrics used include Jaccard coefficient, imprecise function, and monotonicity function. The 10 common algorithms include DC, CC, BC, GC, CAGM, RC, LPP, DR, SP, and DPP, all of which are methods for identifying influential nodes in complex networks.

[0114] This invention calculates influential nodes in a network based on their overall influence. By introducing a propagation dynamics mechanism, it dynamically integrates information interaction probabilities into a complex network model. When the network structure changes, only the inherent influence of the affected nodes and their corresponding information interaction probabilities need to be updated in real time to dynamically calculate the overall influence of the nodes, thereby achieving real-time identification of influential nodes in dynamic networks. Furthermore, the network involved in this invention is an undirected, unweighted network. After calculating the node influence using this invention and obtaining a node importance ranking based on the magnitude of node influence, the results are compared with the benchmark results of the SIR propagation model (Susceptible–Infected–Recovered Model). The following evaluation metrics are used to verify the effectiveness of this invention.

[0115] I. Evaluation Index System

[0116] (1) The accuracy of the influence nodes identified by this invention is evaluated using the Jaccard coefficient index. The formula for calculating the Jaccard coefficient is as follows:

[0117]

[0118] Wherein, X and Y represent the values ​​calculated by step four of this invention and the SIR model, respectively. A collection of influential nodes.

[0119] The Jaccard coefficient is used to assess the similarity between two sets. It can compare the similarity determined by this invention with that determined by the SIR model. Similarity of influence node sets. The more overlapping elements in a set, the higher the Jaccard value. A higher Jaccard value indicates that the influence nodes identified by this invention are more accurate.

[0120] (2) Using an imprecise function to measure the specific calculations made by the method. Influence nodes and the SIR model as determined The differences in influence among influential nodes.

[0121] The imprecision function refers to the difference in influence scores between ranking nodes obtained by the research method and those obtained by the SIR model. A smaller imprecision value indicates a smaller difference in the influence of these nodes, suggesting that the influence of the nodes determined by the research method is more realistic and accurate. The imprecision function is:

[0122]

[0123] in, This refers to the total number of network nodes selected. node, Refers to the definition determined by this method. The sum of the influence of the nodes. This refers to the value calculated by the SIR model. The sum of node influence.

[0124] (3) The monotonicity function is used to explore the node ranking discrimination ability of this method. The larger the monotonicity value, the stronger the node ranking discrimination ability of the specific algorithm. The monotonicity function is represented by the following formula:

[0125]

[0126] in, Indicates the number of network nodes. Represents the set of all nodes in the network. This represents the number of nodes with the same influence value calculated by different methods.

[0127] II: Experimental Dataset

[0128] This experiment selected nine different real-world networks for testing, with varying numbers of nodes in each network. Number of edges First-order average degree Propagation threshold of the target network As shown in Table 1.

[0129] Table 1. Basic Information of the Network Used in the Experiment

[0130]

[0131] III. Experimental Results and Analysis

[0132] 1. Jaccard coefficient results: High consistency in key node identification.

[0133] The results of the Jaccard similarity experiments for each algorithm on 9 real-world networks are as follows: Figures 3-11 As shown, the consistency between the top 10% influential node sets obtained by different algorithms and the SIR model was compared through Jaccard similarity experiments. A higher Jaccard coefficient indicates a greater overlap between the key nodes identified by the algorithm and the SIR simulation results. In the experiment, the horizontal axis represents the infection rate. With network propagation threshold The ratio is shown on the y-axis, with the similarity of the node sets on the ordinate. Results show that in GrQc and Hamster networks, the Jaccard coefficient obtained by the PPCN algorithm proposed in this invention consistently outperforms other algorithms. In EEC, Email, Jazz, and USAir networks, when... At the same time, the PPCN algorithm also showed higher similarity. In other test networks, the curves obtained by the PPCN algorithm were generally in the leading position. In summary, the key nodes identified by the PPCN algorithm under different infection rates are in high agreement with the SIR simulation results, verifying the effectiveness and high robustness of this method in identifying influential nodes.

[0134] 2. Inaccurate function results: significantly smaller influence bias.

[0135] The differences in influence scoring between different algorithms and the SIR model were evaluated through imprecise experiments. The experimental results of each algorithm on the imprecise function in nine real-world networks are as follows: Figures 12-20 As shown, the smaller the inaccuracy value, the closer the influence score of the node obtained by the algorithm is to the SIR simulation result. Figures 12-20 The horizontal axis Indicates the selected top- The proportion of nodes , vertical axis This represents the difference in influence scores for the corresponding node sets, i.e., the imprecise function value. Experimental results from nine networks show that in Erdos, PB, and Hamster networks, the imprecise value obtained by the PPCN method is consistently lower than that of other algorithms. However, in the remaining networks, when... At the same time, the PPCN curve is also generally at the bottom. These results indicate that the PPCN algorithm can identify influential nodes more accurately in most cases, and its smaller imprecision value further verifies the superiority and accuracy of the method in influence assessment.

[0136] 3. Monotonicity Analysis: Node sorting has the strongest distinguishing ability.

[0137] The monotonicity results of each algorithm on the nine networks are shown in Table 2.

[0138] Table 2 shows the monotonicity results of each algorithm on different networks.

[0139]

[0140] In node influence assessment, when multiple nodes have the same influence, their specific ranking is often difficult to distinguish. The monotonicity function experiment aims to evaluate the discriminative ability of different algorithms in ranking network nodes; a higher monotonicity value indicates a stronger discriminative ability. Table 2 lists the monotonicity results of each algorithm in different networks. It can be seen that the PPCN algorithm achieved the highest monotonicity value in seven networks: EEC, Email, Hamster, Jazz, NS, PB, and USAir. In other networks, the PPCN algorithm also achieved a monotonicity of 0.995, demonstrating its generally excellent and robust discriminative ability in node ranking.

[0141] By introducing the influence of node neighbors, a "neighbor diversity" index is defined and combined with the node degree value to effectively distinguish the differences in the inherent influence of nodes, thus solving the defect that different nodes transmit the same influence under the same interaction probability. Simultaneously, this invention defines three effective information interaction modes between node pairs, breaking through the limitation of traditional methods that only allow information to interact along the shortest path, and provides a method for calculating the probability of information interaction between node pairs under these interaction modes. Based on this, by integrating the inherent influence of nodes with the probability of information interaction between node pairs, a comprehensive assessment of the overall influence of nodes is achieved. This scheme not only overcomes the shortcomings of existing methods that rely solely on local topological information, but also introduces a propagation dynamics mechanism, enabling it to effectively identify influential nodes even in dynamically changing complex networks.

[0142] Finally, it should be noted that the above examples are merely some specific embodiments of the present invention. Obviously, the present invention is not limited to the above embodiments and many variations are possible. All variations that can be directly derived or conceived by those skilled in the art from the disclosure of this invention should be considered within the scope of protection of this invention.

Claims

1. A method for identifying influential nodes in complex networks based on neighbor nodes and information interaction, characterized in that... The specific process includes the following: Step S1: Construct an undirected, unweighted complex network based on the network topology data and generate an adjacency matrix; The undirected and unweighted complex network is constructed based on physical facilities and transmission lines in the power system. The nodes of the network correspond to physical facilities in the power system, and the edges of the network correspond to transmission lines or power lines connecting physical facilities. Step S2: Calculate the propagation threshold of the network and the matrix of the number of information interaction paths between node pairs under different path lengths. Then, based on the calculation of the information interaction probability of node pairs under different path lengths, obtain the information interaction probability matrix M between node pairs. Step S3: Based on the node's neighbor information, determine the node's neighbor diversity index, and combine the neighbor diversity index with the node's degree value to calculate the node's inherent influence. ; The method for calculating the neighbor diversity is as follows: in, Represents a node The value of neighborhood diversity, Represents a node The degree value, Represents a node The ranking of neighbor diversity values ​​in descending order. express Nodes in , Represents the set of nodes in the network. Represents a node The neighborhood group, Represents a node The set of neighbors; Step S4: Combine the inherent influence of the nodes With the information interaction probability matrix M, the comprehensive influence of computing nodes ; Step S5: Based on overall influence The nodes in the network are sorted to identify those with critical influence.

2. The method for identifying influential nodes in complex networks based on neighbor nodes and information interaction according to claim 1, characterized in that: The propagation threshold is calculated based on the network's first-order average degree and second-order average degree: in, Indicates the first-order average degree. , This represents the number of edges in the network. Indicates the number of nodes in the network; It represents the second-order average degree.

3. The method for identifying influential nodes in complex networks based on neighbor nodes and information interaction according to claim 2, characterized in that: The information interaction path number matrix includes the path number matrix where the path length between node pairs is 1. A matrix of the number of paths with a path length of 2 And a path count matrix with a path length of 3. : in, Represents the adjacency matrix. Represents a node The degree value, Represents a node The set of neighboring nodes.

4. The method for identifying influential nodes in complex networks based on neighbor nodes and information interaction according to claim 3, characterized in that: The method for calculating the probability of information interaction between nodes under different path lengths is as follows: in, Represents a node and At a distance of The probability of information interaction under the path, The distance between the two nodes is The number of paths.

5. The method for identifying influential nodes in complex networks based on neighbor nodes and information interaction according to claim 4, characterized in that: The probability matrix M of information interaction between node pairs is calculated as follows: 。 6. The method for identifying influential nodes in complex networks based on neighbor nodes and information interaction according to claim 5, characterized in that: The method for calculating the inherent influence is as follows: 。 7. The method for identifying influential nodes in complex networks based on neighbor nodes and information interaction according to claim 6, characterized in that: The method for calculating the overall influence is as follows: ； in, Information interaction probability matrix The elements in It is the set of nodes in the network.

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