Complex network importance node evaluation method based on group interaction

Abstract

The invention discloses a complex network importance node evaluation method based on group interaction. The method comprises the following specific steps: step 1, carrying out community division on a network through a Louvain algorithm; step 2, constructing a Louvain bipartite graph; step 3, obtaining an outgoing transfer matrix and an incoming transfer matrix; step 4, obtaining an extended transfer matrix according to the outgoing transfer matrix and the incoming transfer matrix; 5, expanding the transfer matrix to obtain an enhanced transfer matrix; step 6, calculating the importance score of each node; 7, arranging the nodes in the network in a descending order according to the importance score of each node; and step 8, identifying important nodes of the network through a network disintegration algorithm. According to the method, based on group interaction, the interaction between nodes which are not directly connected is considered, the random walk is expanded to the Louvain bipartite graph, and the concepts of outgoing walk and incoming walk are added; and in combination with a network disintegration algorithm, the key nodes in the network are efficiently and accurately identified, and the robustness and the stability are high.

Description

Technical Field

[0001] The present invention belongs to the technical field of network evaluation methods, and particularly relates to an evaluation method for important nodes in complex networks based on group interaction. Background Art

[0002] The heterogeneity and scale-free characteristics of complex network connections indicate that the influence of nodes in complex systems is uneven, that is, different nodes play very different functions and roles. Therefore, the identification of key nodes is a hot topic in the field of complex networks. Most studies in network science and important node identification mainly focus on systems with pairwise topological structures, that is, modeling the network as a graph composed of a node set and edges. However, the functions of many network systems are affected or determined by community structure interactions, and such interactions occur not only between node pairs but also involve larger node sets. Examples of these community structure effects include: product recommendations from multiple friends in social networks, information transmission that requires the coordination of many neurons in brain networks, and hunting behaviors involving multiple organisms in ecological competition networks. Group interaction is an important part of complex systems, but the classical pairwise structure is not sufficient to accurately capture or simulate these group dynamics. In addition, in cases where nodes share similar pairwise connections but exhibit different roles in higher-order structures, existing methods may not be able to effectively distinguish node influence. Therefore, research on community structure interactions in complex systems has attracted extensive attention in the scientific community in recent years.

[0003] In networks considering pairwise nodes, three main types of methods, namely neighborhood-based centrality, path-based centrality, and iterative refinement centrality, are mainly used to identify important nodes. In addition to the above three types of important node identification methods, methods based on node removal and contraction evaluate node importance by removing or contracting nodes. After a node is removed, if the connectivity of the network drops significantly, then the node is considered important. The node contraction rule is to merge a node and its neighbors into a new node, and evaluate node importance by observing the change in network cohesion. Other algorithms also include: models based on graph neural networks, and methods inspired by quantum entanglement and gravitational theory.

[0004] Due to the complexity of community structures, there are relatively few literatures considering the influence and role of community structures on node importance. The consideration of higher-order structures is based on simplices, however, interactions between groups may also occur within larger groups. For example, in the same school, even two people who do not know each other may transmit information through mutually known colleagues, and such interactions within groups are often ignored.

[0005] Random walk dynamics is the basis for many important node identification algorithms and has recently been extended to networks with more complex structures. However, current methods only allow nodes to walk between adjacent-order simplices, making them inflexible and difficult to scale. Therefore, there is an urgent need to develop new random walk models and node ranking methods that consider higher-order structures in any order to better understand the underlying dynamics and provide a more comprehensive perspective on network behavior. Summary of the Invention

[0006] The object of the present invention is to provide a method for evaluating important nodes in complex networks based on group interactions, which solves the problems in existing methods that only consider the interactions of directly connected paired nodes and only allow nodes to walk between adjacent-order simplices.

[0007] The technical solution adopted by the present invention is a method for evaluating important nodes in complex networks based on group interactions, and the specific steps are as follows: Step 1, partition the network into communities by the Louvain algorithm; Step 2, according to the community partition result, add class nodes and edges to construct a Louvain bipartite graph; Step 3, define an extended random walk to obtain an out-transition matrix and an in-transition matrix; Step 4, obtain an extended transition matrix according to the out-transition matrix and the in-transition matrix; Step 5, obtain an enhanced transition matrix by the weighted classical transition matrix and the extended transition matrix; Step 6, calculate the importance score of each node; Step 7, sort the nodes in the network in descending order according to the importance score of each node; Step 8, identify the important nodes of the network by the network disintegration algorithm. The characteristics of the present invention also lie in: The specific process of Step 1 is as follows: Step 1.1, initially regard each node in the network as a community, so the number of communities is the same as the number of nodes; Step 1.2, then successively merge each node with all its adjacent nodes together to form a new community, calculate the modularity gain of each new community , and put the current node into the community where the adjacent node with the largest modularity gain is located; Among them, assuming a node moves to the community , the obtained modularity gain has the following expression: (1) In formula (1), is in the community The sum of the weights of the links within o. When the weight is 1, it is equal to the modularity. In the initial case, when a node forms a community by itself, it is the connection from the node to itself, but still requires the start weight and the end weight (even when the start and end are the same node, the weight for an acyclic graph is 0); is the sum of the weights of the links associated with the nodes in the community; is the sum of the weights of the links associated with the node ; is the sum of the links from the node connected to the nodes in the community; represents the sum of the weights of all edges in the network. When the weight is 1, represents the number of all edges in the network; Step 1.3, iterate Step 1.2 until the modularity gain is stable, that is, the community to which all nodes belong no longer changes; Step 1.4, compress all the nodes within each new community that no longer changes in Step 1.3 into a supernode. The edge weight of the supernode is the sum of the edge weights of all the nodes within its corresponding new community. All the supernodes form a new network; Step 1.5, continuously repeat the operations of Steps 1.1 - 1.3 on the new network formed in Step 1.4 until the modularity no longer increases. Finally, taking each community as a category of the original network, the number of categories obtained for the division of the original network is obtained, as well as the category to which each original node belongs.

[0008] The specific process of Step 2 is as follows: According to the categories obtained from the division of the original network in Step 1.5, add an independent node for each community. This independent node serves as a class node, that is, add class nodes. Next, for the original nodes, if the node j belongs to the community , , then add a new edge between the node j and the class node i . Through the class nodes and the new edges, the Louvain bipartite graph is obtained, and the expression is: (2) In formula (2), V represents the set of nodes in the original network, W represents the set of class nodes, represents the set of new edges.

[0009] In step 3, the expression of the out-going transition matrix is: (3) where , , ; In the formula, represents the random walk probability from the original node to the class node ; represents the degree of the original node in the Louvain bipartite graph; represents the incidence matrix, represents that the original node belongs to the community , 0 represents not belonging to the community ; is a diagonal matrix, and its diagonal elements are the degrees of the nodes in the Louvain bipartite graph.

[0010] In step 3, the expression of the in-coming transition matrix is: (4) where ; In the formula, represents the number of nodes contained in the community i ; is a diagonal matrix, and its diagonal elements are equal to the number of nodes connected by the class nodes.

[0011] In step 4, the expression of the extended transition matrix is: (5).

[0012] In step 5, the expression of the enhanced transition matrix is: (6); where ; In the formula, A is the adjacency matrix of the network; De is the degree matrix; C is the classical transition matrix; is the weight, takes values from 0 to 1. When , it represents only considering the pairwise structure information of the network. When , it represents only considering the community structure information of the network.

[0013] The specific process of step 6 is: calculate the steady-state probability distribution of the enhanced random walk process on the Louvain bipartite graph through formula (7). When the iteration of formula (7) terminates, the importance score of each node can be obtained; Formula (7) is as follows: (7) In formula (7), is a vector, and its th term represents the probability of reaching node at step t.

[0014] The specific process of step 8 is as follows: The nodes sorted in step 7 are removed one by one from largest to smallest. The removed nodes are the target nodes. The target nodes and the nodes that lose their link relationships in the network due to the removal of the target nodes are removed from the network to obtain the remaining network. Calculate the largest connected component in the remaining network until the number of nodes contained in the largest connected component GCC in the network is less than or equal to 1% of the number of nodes in the network. Then, the removed target nodes are the minimum important node set of the network.

[0015] The beneficial effects of the present invention are as follows: The method for evaluating important nodes in a complex network based on group interaction of the present invention considers the interaction between nodes that are not directly connected within a community, adds the concepts of out-going walk and in-coming walk, and extends the random walk to the Louvain bipartite graph, so as to be able to efficiently and accurately identify the key nodes in the network, with strong robustness and stability, and can stably play its advantages in different network data, not affected by the structural complexity, providing a reliable basis for network analysis. Brief Description of the Drawings Figure 1 is a flowchart of the method for evaluating important nodes in a complex network based on group interaction of the present invention; Figure 2 is a construction and structure diagram of the Louvain bipartite graph in the method for evaluating important nodes in a complex network based on group interaction of the present invention; Figure 3 is a schematic diagram of random walk, extended random walk, and enhanced random walk in the method for evaluating important nodes in a complex network based on group interaction of the present invention; Figure 4 is a bar chart of the experimental result comparison of Example 6. Detailed Embodiments

[0016] The present invention will be described in detail below with reference to the drawings and specific embodiments.

[0017] Example 1 The method for evaluating important nodes in a complex network based on group interaction of the present invention, as Figure 1 shown, the specific steps are as follows: Step 1, divide the network into communities by the Louvain algorithm; Step 2: According to the community division result, add class nodes and connecting edges to construct a Louvain bipartite graph; Step 3: Define an extended random walk to obtain an outgoing transition matrix and an incoming transition matrix; Step 4: Obtain an extended transition matrix based on the outgoing transition matrix and the incoming transition matrix; Step 5: Obtain an enhanced transition matrix by weighting the classical transition matrix and the extended transition matrix; Step 6: Calculate the importance score of each node; Step 7: Sort the nodes in the network in descending order according to the importance score of each node; Step 8: Identify the important nodes of the network through a network disintegration algorithm.

[0018] Example 2 Based on Example 1, the specific process of Step 1 is as follows: Step 1.1: Initially, regard each node (original node) in the network as a community, so the number of communities is the same as the number of nodes; Step 1.2: Then, successively merge each node with all its adjacent nodes together to form a new community, calculate the modularity gain of each new community , and put the current node into the community where the adjacent node with the largest modularity gain is located; Among them, assuming a node moves to community C, the obtained modularity gain Q ΔQ is expressed as: (1) In formula (1), w_{in}(C) is the total weight of the links within community C. When the weight is 1, w_{in}(C) is equal to the modularity. If it is the initial situation, that is, when a node is a community by itself, w_{in}(C) is the connection of this node to itself, but still requires the start weight and the end weight (even if the start and end points are the same node at this time, the weight for an acyclic graph is 0); w_{t}(C) is the total weight of the links associated with the nodes in community C; w_{t}(i) is the total weight of the links associated with node i; w_{out}(i, C) is the sum of the links from node i to the nodes in community C; w_{all} represents the sum of the weights of all edges in the network. When the weight is 1, E represents the number of all edges in the network; Step 1.3. Iterate Step 1.2 until the modularity gain is stable, that is, the communities to which all nodes belong no longer change; Step 1.4. Compress all nodes within each community that no longer changes in Step 1.3 into a supernode. The edge weight of the supernode is the sum of the edge weights of all nodes within its corresponding community. All supernodes form a new network; Step 1.5. Continuously repeat the operations of Steps 1.1 - 1.3 on the new network formed in Step 1.4 until the modularity no longer increases. Finally, take each community as a category of the original network, and the number of categories into which the original network is partitioned can be obtained , as well as the category to which each original node belongs.

[0019] Example 3 Based on Example 2, as Figure 2 shown, the specific process of Step 2 is as follows: According to the categories into which the original network is partitioned obtained in Step 1.5, add one independent node for each community. This independent node serves as a class node, that is, class nodes are added. Next, for the original nodes, if the original node j belongs to community , , then add a new edge between the original node j and the class node . Through the class nodes and the new edges, a Louvain bipartite graph is obtained, and the expression is: (2) In formula (2), V represents the set of original network nodes, W represents the set of class nodes, represents the set of new edges; The Louvain bipartite graph can capture the indirect relationships between nodes by introducing class nodes and connecting edges.

[0020] Example 4 Based on Example 3, as Figure 3 shown, the specific process of Step 3 is as follows: Define an extended random walk. The steps of the extended random walk include performing an extended random walk between the original nodes and class nodes in the network. The random process can capture potential topological properties. According to the direction of the extended random walk, the extended random walk is divided into two parts: an outgoing walk and an incoming walk; Outgoing walk process: It involves traversing from the original nodes in the Louvain bipartite graph to their corresponding class nodes. During the outgoing walk process, the importance of each node is evenly distributed among the communities it belongs to; The expression of the out-transfer matrix is as follows: (3) Wherein, , , ; In the formula, represents the walking probability from the original node to the class node ; represents the degree of the original node in the Louvain bipartite graph; represents the incidence matrix, represents that the original node belongs to the community , 0 represents not belonging to the community ; is a diagonal matrix, and its diagonal elements are the degrees of the nodes in the Louvain bipartite graph; Incoming walking process: The process of transmitting information from class nodes. In this process, the importance of each community is evenly distributed among the nodes it contains, which ensures that each node receives the same importance as its belonging community; The expression of the in-transfer matrix is as follows: (4) Wherein, ; In the formula, represents the number of nodes contained in the community i ; is a diagonal matrix, and its diagonal elements are equal to the number of nodes connected by the class nodes.

[0021] The out-transfer matrix focuses on how the original node distributes its importance to the communities containing it, reflecting the participation degree of the node in the community. The in-transfer matrix focuses on how the class node feedbacks its importance to its member nodes, reflecting the influence and contribution of the community to the node.

[0022] Embodiment 5 Based on Embodiment 4, in step 4, the expression of the extended transfer matrix is as follows: (5).

[0023] Embodiment 6 Based on Embodiment 5, in step 5, the expression of the enhanced transfer matrix is as follows: (6); Wherein, ,De

[0024] where A is the adjacency matrix of the network; De is the degree matrix; C is the classical transition matrix; is the weight, takes values from 0 to 1. When , it represents only considering the pairwise structure information of the network. When , it represents only considering the community structure information of the network.

[0025] The classical transition matrix C describes the movement process of random walkers in the graph by calculating the transition probability between nodes, thereby reflecting the pairwise structure characteristics of the graph; The random walk performed on the network represented by the Louvain bipartite graph only captures the community characteristics of the network while ignoring the pairwise characteristics. Therefore, it is considered to perform random walks simultaneously on the bipartite graph and the classical pairwise graph to obtain a comprehensive understanding of the network characteristics.

[0026] Example 7 Based on Example 6, the specific process of step 6 is as follows: By enhancing the transition matrix M, the pairwise and community interactions in a given network can be captured simultaneously; Calculate the steady-state probability distribution of the enhanced random walk process on the Louvain bipartite graph through formula (7). When the iteration of formula (7) terminates, the importance score of each node can be obtained; Formula (7) is as follows: (7) In formula (7), is a vector, and its th term represents the probability of reaching node at step t. Once the distribution converges, that is (in the present invention, = 0.01) is adopted, the iteration terminates.

[0027] Example 8 Based on Example 7, the specific process of step 8 is as follows: Remove the sorted nodes from step 7 one by one in descending order. The removed nodes are the target nodes. Remove the target nodes and the nodes whose link relationships with the network are lost due to the removal of the target nodes from the network to obtain the remaining network. Calculate the largest connected component in the remaining network until the number of nodes included in the largest connected component GCC in the network is less than or equal to 1% of the number of nodes in the network. Then the removed target nodes are the set of the least important nodes in the network.

[0028] The descending order in step 7 means that in the subsequent node removal process, those nodes with the highest scores will be preferentially removed because they are considered to have the greatest impact on the network structure.

[0029] The present invention gradually destroys the network structure through node importance ranking, and through the process of network disintegration, it is possible to deeply understand the structural characteristics of the network, the role of important nodes, and the robustness and vulnerability of the network in the face of node removal attacks, providing valuable reference and guidance for network optimization, protection, and design.

[0030] Example 9 The effects of the present invention can be specifically illustrated through simulation experiments: 1. Experimental conditions The experiment used a computer equipped with a CPU R7-4600U processor, 16 GB of RAM, Windows 11 system, and Pycharm 2024.1.1.

[0031] The dataset (undirected network) used in the experiment is shown in Table 1: Table 1

[0032] 2. Experimental conditions First, read the network data from the txt file of the dataset and construct an initial graph, which is parsed into a list of edges. Each edge consists of two nodes, representing the connection relationship between the nodes. Then, calculate the classical transition matrix and the extended transition matrix of the network. The former is used to describe the pairwise interactions between nodes, and the latter combines the community effect to more comprehensively reflect the network structure. By linearly combining these two matrices according to the weight coefficient, an enhanced transition matrix is obtained, and the node importance is evaluated using random walk. Different values of the weight parameter allow flexible adjustment of the relative contributions of pairwise interactions and community effects. In the experiment, s = 0.53 was fixed, and the node importance ranking results under different community partitioning methods were compared, and the results were normalized for analysis and comparison, so as to deeply understand the structural characteristics of complex networks.

[0033] Comparative Example 1 A method with relatively obvious advantages compared with the current traditional centrality index was selected. Considering the influence of the simplex structure in the network on the importance of network nodes, the network was first partitioned according to the simplex to construct a high-order bipartite graph, a random walk matrix was constructed based on upstream random walk and downstream random walk, and the network nodes were ranked according to the matrix.

[0034] The specific process is as follows: (1)Partition the network according to the simplex, and a simplex is a class; (2)Each class is abstracted into a class node. If the network contains p simplices, it is divided into p classes, that is, p nodes are added. An edge is added between each node in the original network and its corresponding class node to construct a higher-order bipartite graph; (3)According to the definitions of upward walk and downward walk in the concept of higher-order random walk, the upstream transition matrix and the downstream transition matrix are obtained; (4)The upstream transition matrix is multiplied by the downstream transition matrix to obtain the two-step transition matrix; (5)The weighted two-step random walk and the traditional random walk are combined to obtain the higher-order enhanced transition matrix; (6)According to the higher-order enhanced transition matrix, the importance score of each node is calculated by formula (7); (7)The nodes in the network are sorted in descending order according to the importance score of each node; (8)The network disintegration algorithm is used to identify the key nodes.

[0035] This method classifies according to simplices, and the number of classes it divides is much more than that of the present invention, that is, the number of added nodes is much larger, and at the same time, the number of added edges is much more than that of the method of the present invention, which will increase the calculation cost and affect the timeliness of calculation. This shortcoming is even more disastrous for network problems with a large amount of data itself.

[0036] Comparative Example 2 To illustrate the advantages of the method of the present invention, that is, the community structure does have an impact on the node importance, different community partitioning methods are selected, the network is partitioned into communities using k-means, a bipartite graph is constructed, the influence ranking of nodes is obtained according to the transition matrix, and finally the network disintegration algorithm is used to identify the key nodes.

[0037] The specific steps are as follows: (1)Partition the network according to k-means; (2)Each class is abstracted into a class node. If the network contains β classes, that is, β nodes are added. An edge is added between each node in the original network and its corresponding class node to construct a bipartite graph; (3)According to the definitions of out-going walk and in-coming walk in the concept of extended random walk, the out-going transition matrix and the in-coming transition matrix are obtained; (4)Combining the out-going transition matrix and the in-coming transition matrix, the extended transition matrix is obtained; (5)Weighting the extended random walk and the traditional random walk theory to obtain the enhanced transition matrix; (6)Calculate the importance score of each node; (7)The nodes in the network are sorted in descending order according to the importance score of each node; (8)The network disintegration algorithm is used to identify the key nodes.

[0038] Among them, steps (3) to (8) are the same as those in steps 3 to 8 of the present invention.

[0039] For the same network, the number of classifications of this method is similar to that of the method of the present invention. However, due to the different classes to which specific nodes are assigned, different results are obtained, indicating that not only group interaction cannot be ignored, but the group structure does have an impact on node importance. A more accurate division leads to better results.

[0040] Finally, by removing important nodes one by one in the experiment and observing the change in the largest connected component (GCC) of the network graph, the impact of node importance on network connectivity is studied. The termination condition is set for the size of the GCC (in this experiment, it is 1% of the original network, that is, when the size of the GCC of the current network is less than or equal to 1% of the number of nodes in the original network, the disintegration of the network stops). The nodes are removed in turn using the node ranking, and the updated network size and GCC are recorded until the termination condition is reached. Finally, based on the nodes required to disintegrate the network, the critical minimum node set of the network is obtained, and the effectiveness of different methods is analyzed.

[0041] 3. Experimental Results Parameter settings: In the present invention It is set to the random number 0.58. To make the comparison more fair (the information interaction of nodes is not only related to the number of communities but also to the specific nodes within the communities), for the k-means algorithm, it is assumed that the number of classifications is known in advance. That is, the number of classifications of k-means in Comparative Example 2 is set as follows: for the datasets USAir, jazz, neural, Grid, and Lastfm, the number of classifications is set to 50, 62, 30, 16, and 98 respectively.

[0042] By comparing different methods, the following results are obtained:

[0043]

[0044]

[0045]

[0046]

[0047] It can be seen from the experimental results that the method of the present invention shows obvious advantages in terms of the number of nodes required to disintegrate the network. Specifically: In the disintegration experiments of multiple network datasets, the method of the present invention generally exhibits superior performance. Only a few nodes need to be removed to disintegrate the network, highlighting its efficiency in identifying key nodes. The smallest node set that can disintegrate the network is the key node set in the network. The fewer the number of key nodes, the more important the individual nodes found, and the more crucial the nodes found by this method are for the entire network structure and performance. In the USAir network, the algorithm of the present invention only needs to remove 159 nodes, which is more efficient than 176 nodes in Comparative Example 1 and 198 nodes in Comparative Example 2; in the jazz network, it performs equivalently to Comparative Example 2 but is better than Comparative Example 1; in the neural network, the algorithm of the present invention also outperforms Comparative Example 1 and Comparative Example 2; in the large-scale Grid network and Lastfm network, the algorithm of the present invention still maintains its advantage. It should be noted that the method of the present invention has the same result as Comparative Example 2 in jazz, Grid, and LastFm. However, this result is because we set a relatively accurate number of clusters for the k-means algorithm in advance. For general problems, the number of clusters cannot be known in advance, and actually the result of Comparative Example 2 is inferior to the method of the present invention.

[0048] The bar chart of the percentage of the key node set of each method in the overall network is as Figure 4 shown, which indicates that the algorithm of the present invention can disconnect the network with fewer nodes removed in networks of different scales and types. It effectively identifies the key node set that has the greatest impact on network connectivity, fully proving that the method of the present invention measures the importance of nodes more accurately and demonstrating its strong application potential in the field of network analysis.

[0049] In summary, using the Louvain algorithm to partition the network into communities, increasing nodes and edges according to the number of communities, extracting the network community structure information according to the outgoing random walk and incoming random walk, thereby obtaining the importance ranking of nodes, and combining the network disintegration algorithm to identify the influence of network nodes is effective and performs excellently. Our method has strong adaptability and good robustness, and its ability to efficiently identify key nodes makes it have important application value in the fields of network analysis, network control, etc.

Claims

1. A method for evaluating important nodes in a complex network based on group interaction, characterized in that The specific steps are as follows: Step 1, perform community partitioning on the network through the Louvain algorithm; Step 2, according to the community partitioning result, add class nodes and connecting edges to construct a Louvain bipartite graph; Step 3, define an extended random walk to obtain an out-transfer matrix and an in-transfer matrix; Step 4, obtain an extended transfer matrix based on the out-transfer matrix and the in-transfer matrix; Step 5, obtain an enhanced transfer matrix through a weighted classical transfer matrix and the extended transfer matrix; Step 6, calculate the importance score of each node; Step 7, sort the nodes in the network in descending order according to the importance score of each node; Step 8, identify the important nodes of the network through a network disintegration algorithm.

2. The method for evaluating important nodes in a complex network based on group interaction according to claim 1, wherein The specific process of Step 1 is as follows: Step 1.1, initially consider each node in the network as a community, so the number of communities is the same as the number of nodes; Step 1.2, then successively merge each node with all its adjacent nodes together to form a new community, and calculate the modularity gain of each new community , and put the current node into the community where the adjacent node with the largest modularity gain is located; Among them, assume a node moves to community Co, and the modularity gain is expressed as: （1） In formula (1), is the total weight of the links within the community o. When the weight is 1, it is equal to the modularity. In the initial case, that is, when a single node forms a community, it is the connection of the node to itself, but still requires the starting weight and the ending weight; is the total weight of the links associated with the nodes in the community ; is the total weight of the links associated with the node ; is the total of the links from the node to the nodes in the community ; represents the sum of the weights of all the edges in the network. When the weight is 1, represents the number of all the edges in the network; Step 1.3, iterate Step 1.2 until the modularity gain is stable, that is, the communities to which all nodes belong no longer change; Step 1.4, compress all the nodes in each new community that no longer changes in Step 1.3 into a super node. The edge weight of the super node is the sum of the edge weights of all the nodes in its corresponding community. All the super nodes form a new network; Step 1.5, continuously repeat the operations of Steps 1.1 to 1.3 on the new network formed in Step 1.4 until the modularity no longer increases. Finally, take each community as a category of the original network, and then the number of categories obtained by partitioning the original network can be obtained. , as well as the category to which each original node belongs.

3. The method for evaluating important nodes in a complex network based on group interaction according to claim 2, wherein The specific process of step 2 is as follows: According to the categories obtained by the original network partition in step 1.5, one independent node is added for each community, and this independent node serves as a class node, that is, class nodes are added. Next, for the original nodes, if a node j belongs to community , , then a new edge is added between node j and the class node i . Through the class node and the new edge, the Louvain bipartite graph is obtained, and the expression is: （2） In formula (2), V represents the set of original network nodes, and W represents the set of class nodes, represents the set of new edges.

4. The method for evaluating important nodes in a complex network based on group interaction according to claim 3, wherein In Step 3, the expression of the out-transfer matrix is: （3） Among them, , , ; In the formula, represents the walking probability from the original node to the class node ; represents the degree of the original node in the Louvain bipartite graph; represents the incidence matrix, representing that the original node belongs to the community , 0 represents not belonging to the community ; is a diagonal matrix, and its diagonal elements are the degrees of the nodes in the Louvain bipartite graph.

5. The method for evaluating important nodes in a complex network based on group interaction according to claim 4, wherein In Step 3, the expression of the in-transfer matrix is: （4） Among them, ; In the formula, represents the number of nodes i contained in the community; is a diagonal matrix, and its diagonal elements are equal to the number of nodes connected to the class node.

6. The method for evaluating important nodes in a complex network based on group interaction according to claim 5, wherein In Step 4, the expression of the extended transfer matrix is: （5）。 7. The method for evaluating important nodes of a complex network based on group interaction according to claim 6, wherein In Step 5, the expression of the enhanced transfer matrix is: （6）； Among them, , De ; Wherein, A is the adjacency matrix of the network; De is the degree matrix; C is the classical transition matrix; is the weight, takes values from 0 to 1. When , it represents only considering the pairwise structure information of the network. When , it represents only considering the community structure information of the network.

8. The method for evaluating important nodes in a complex network based on group interaction according to claim 7, characterized in that The specific process of Step 6 is as follows: calculate the steady-state probability distribution of the enhanced random walk process on the Louvain bipartite graph through formula (7). When the iteration of formula (7) terminates, the importance score of each node can be obtained; Formula (7) is as follows: （7） In formula (7), is a vector, and its -th term represents the probability of reaching node t at step .

9. The method for evaluating important nodes in a complex network based on group interaction according to claim 8, characterized in that The specific process of Step 8 is as follows: sequentially remove the nodes sorted in Step 7 from largest to smallest. The removed nodes are the target nodes. Remove the target nodes and the nodes that lose their link relationships in the network due to the removal of the target nodes from the network to obtain the remaining network. Calculate the largest connected component in the remaining network until the number of nodes contained in the largest connected component GCC in the network is less than or equal to 1% of the number of nodes in the network. Then the removed target nodes are the minimum important node set of the network.

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