Complex network node influence sorting method and system based on structure entropy

Abstract

The invention relates to a complex network node influence sorting method and system based on structure entropy, and belongs to the technical field of social network analysis. The method comprises the following steps: constructing a social network graph according to a data set, and carrying out community discovery by utilizing two-dimensional structure entropy to obtain stable overlapping communities; calculating the influence of the nodes in the community and the influence of the nodes across the community, and performing linear combination on the influence of the nodes in the community and the influence of the nodes across the community to obtain a comprehensive influence value of each node; and sorting all the nodes according to the comprehensive influence value, and identifying the key node with the maximum influence in the social network. According to the method, the importance of the nodes in the social network is evaluated by measuring the two-dimensional structure entropy change of the nodes in the communities and among the communities, so that the key nodes are identified and sorted, and the method for effectively identifying and sorting the key nodes is provided for obtaining the important nodes in the social network.

Description

Technical Field

[0001] The present invention relates to a complex network node influence ranking method and system based on structural entropy, belonging to the technical field of social network analysis. Background Art

[0002] With the development of social network, information dissemination and interaction between people have become more convenient and efficient. In social networks, the ranking of node influence not only plays an important role in information dissemination and public opinion guidance, but also has wide applications in viral marketing, public safety and social management. How to accurately evaluate and rank the influence of nodes is crucial to optimizing the function and utility of social networks.

[0003] There are two main methods for identifying key nodes in the network. One is based on local attributes. Common local methods include degree centrality and local structural entropy. Degree centrality is the most direct metric to characterize node centrality. The degree centrality is used to represent the influence of the node. Local structural entropy considers the information of first-order and second-order neighboring nodes and uses the local structural attributes of the entire network node, rather than the properties of the node itself. The other is based on global attributes. Common ones include betweenness centrality and PageRank algorithm. Betweenness centrality describes the frequency of information passing through the node when it propagates in the social network. It can better reflect the topological characteristics of the node. The PageRank algorithm uses neighbor nodes to characterize the influence of the node. However, the nodes selected by the local method only consider local information, and the influence of the node is only reflected in the clustered community, which easily leads to the omission of overall information. When dealing with large-scale networks, these global methods have problems such as high computational complexity and ignoring node attributes. Summary of the invention

[0004] The present invention provides a method and system for ranking the influence of complex network nodes based on structural entropy. The method uses two-dimensional structural entropy to measure the influence changes of nodes in different community structures, comprehensively considers the local authority of the nodes in their respective communities and the breadth of influence across communities, and provides a method for effectively identifying and ranking key nodes.

[0005] The technical solution of the present invention is: a complex network node influence ranking method based on structural entropy, the method comprising:

[0006] Step 1: Build a social network graph based on the data set, use two-dimensional structural entropy to discover communities, and obtain stable overlapping communities, so that each node and community is in a stable state, and ensure that each network node belongs to one or more communities;

[0007] Step 2: Calculate the influence of the node within the community and the influence of the node across communities, and perform a linear combination of the influence of the node within the community and the influence of the node across communities to obtain the comprehensive influence value of each node; the influence of the node consists of two parts, one is the influence of the node within the community, and the other is the influence of the node across communities. The influence within the community is the change in the structural entropy of the community after the node leaves the community, and the cross-community influence is the sum of the changes in the structural entropy of all target communities after the node joins the target community;

[0008] Step 3: Sort all nodes according to their comprehensive influence values ​​and identify the key nodes with the greatest influence in the social network.

[0009] Furthermore, the Step 1 includes:

[0010] Step 1.1. Select a dataset containing social network data, including nodes and the relationships (edges) between nodes, use the social network data to build a graph structure, use the network analysis library NetworkX to create a graph, and add nodes and edges to the graph;

[0011] Step 1.2, use the community discovery algorithm based on two-dimensional structural entropy to obtain multiple overlapping communities. When the two-dimensional structural entropy of each community remains stable, keep the existing structure of the community, calculate the two-dimensional structural entropy of each community and the two-dimensional structural entropy of the entire network, obtain the adjacent community matrix of the target node, and obtain a stable overlapping community.

[0012] Furthermore, the Step 2 includes:

[0013] Step 2.1. Calculate the two-dimensional structural entropy of each community and obtain the adjacent community matrix of the target node. When the node is moved from the existing community to the target community, the volume and number of boundary edges of the original community are g respectively. in and v in , and then after the node leaves the original community, the community volume and the number of community border edges after the node leaves the community are g in ' and v in ', the influence of the node in the community after leaving the community is ΔSE in ;

[0014] g in '=g in +d-2n in (1)

[0015] v in '=v in +d (2)

[0016]

[0017] where d is the number of edges that the node is connected to; n in represents the number of neighbors of the node in the current or target community, that is, the number of connections between the node and other nodes in the community; vol is the volume of the entire graph, that is, the sum of the degrees of all nodes in the graph;

[0018] Step 2.2: According to the node's adjacent community matrix, the node target community matrix is ​​traversed in turn. For the target community, the volume and number of boundary edges of the community before the node joins are g and g respectively. cross and v cross , the community volume and the number of community border edges after the node joins the target community are g cross ' and v cross ', after updating the volume and number of boundary edges of the community, the node moves from the current community to the target community or becomes a community on its own. For each node after the move, the influence of the node across communities is calculated, which is ΔSE cross ;

[0019] g cross '=g cross -d+2n in (4)

[0020] v cross '=v cross -d (5)

[0021]

[0022] Step 2.3: Take the weighted sum of the influence of the node within the community and the influence of the node across communities to obtain the comprehensive influence of node i;

[0023] The influence of a node is composed of its influence within the community and its influence across communities. However, the proportions of the two are not necessarily equal. A network influence factor α is selected to balance the weights of the two, and the comprehensive influence of node i is obtained as follows:

[0024]

[0025] ΔSE in Represents the influence of the node in the community, that is, the authority of the node in the community; ΔSE cross Represents the influence of the node across communities. The node has influence not only in its own community, but also in other communities. adj_div represents the set of all other target communities.

[0026] Step 2.4: According to the IC propagation model, set α∈[0,1] with a step size of 0.01, and traverse the network influence factor α in turn to obtain the final number of nodes after propagation through the IC propagation model. Determine the network influence factor α with the largest number of propagated nodes on multiple data sets, thereby determining the proportion of influence within the community and cross-community influence on the node influence, and then execute Step 2.3.

[0027] Furthermore, the Step 3 includes:

[0028] Step 3.1. After obtaining the comprehensive influence of each node in the community according to the network influence factor, sort the nodes in the social network according to the comprehensive influence of the nodes. The greater the influence of the node, the more important the node is in the social network. When maximizing the influence, the higher the ranking of the node, the stronger its communication ability. Finally, the comprehensive influence ranking result of each node is obtained; the sorted node list is:

[0029] V sorted =SORT desc (V,key=INF(i)) (8)

[0030] Among them, V sorted It is a sorted list of nodes, in which the nodes are arranged in descending order of comprehensive influence; SORT desc is a sorting function, which means sorting the nodes in descending order; V is a set or list containing all nodes, and is also a parameter in the key sorting function, which means sorting the nodes according to the INF value. The node list is the collection of all nodes in the social network. Through the sorting operation, the nodes in the node list are arranged from high to low according to their comprehensive influence, forming a sorted list, that is, V sorted .

[0031] The invention uses two-dimensional structural entropy to perform community discovery on the basis of community discovery results and calculates the influence of nodes in existing communities and target communities, including the two-dimensional structural entropy of the current community and the two-dimensional structural entropy of the entire network; after the node leaves the original community and joins the target community, the entropy changes of the original community, the target community and the entire network are recalculated; the entropy change values ​​of each community are linearly combined to obtain the influence of each node, and the nodes are sorted; the invention evaluates the importance of nodes in social networks by measuring the changes of the two-dimensional structural entropy of nodes within and between communities, thereby identifying and sorting key nodes, and providing an effective method for obtaining important nodes in social networks.

[0032] The present invention also provides a system for ranking the influence of complex network nodes based on structural entropy, and the system includes: a module for executing the above-mentioned method for ranking the influence of complex network nodes based on structural entropy.

[0033] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned method for ranking the influence of complex network nodes based on structural entropy when executing the program.

[0034] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the method for ranking the influence of complex network nodes based on structural entropy is implemented.

[0035] The present invention also provides a computer program product, including a computer program, which, when executed by a processor, implements the above-mentioned complex network node influence ranking method based on structural entropy.

[0036] The beneficial effects of the present invention are:

[0037] 1. The present invention solves the problem that the previous methods have limitations in identifying key nodes in the network. Local attribute methods such as degree centrality and local structural entropy only consider local information of nodes and are prone to omit overall information. It also solves the problem that the global attribute method has high computational complexity, is not suitable for large-scale networks, and ignores node attributes.

[0038] 2. The present invention accurately evaluates the comprehensive influence of each node by calculating the entropy change when the node moves from the original community to the target community and combining it with the entropy change of the entire network; this method can more accurately identify key nodes in social networks, providing a comprehensive analytical perspective and helping to deeply understand the network structure and node roles;

[0039] 3. Through the adjustment of linear combination and weight parameters, the present invention provides a flexible network analysis tool that adapts to different network structures and research needs. While improving the accuracy of community discovery, it can optimize the network structure, enhance network stability, and support precise intervention strategies, such as applications in social media, public health, and network security.

[0040] 4. Compared with traditional methods, the present invention not only considers the local information of nodes, but also incorporates the global information of social networks, thereby effectively supplementing the overall information omission problem caused by relying only on local information; in addition, the present method significantly improves the speed of processing nodes in large-scale networks and reduces the computational complexity;

[0041] 5. By comparing the number of common nodes of different methods, the consistency of the nodes selected by the method of ranking the influence of nodes based on two-dimensional structural entropy and the nodes selected by other methods was verified; according to the final number of activated nodes obtained by different methods through the IC propagation model, the effectiveness of the influential nodes selected by the method of ranking the influence of nodes based on two-dimensional structural entropy in the IC propagation model was proved;

[0042] 6. This paper proposes an influence ranking method that comprehensively considers local and global attributes. This method defines node influence by the influence of nodes within the community and across communities and ranks nodes by importance, effectively overcoming the limitations of previous methods.

[0043] 7. This method is not only innovative in theory, but also shows extremely high practical value in practical applications, especially in the fields of network structure analysis, information diffusion prediction and network security. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a schematic diagram of the specific structure of the recognition model in the present invention;

[0045] Figure 2 The results of consistency comparison and verification of the top 10 nodes in the Facebook social network and CA-GrQc social network influence ranking obtained by the method of the present invention and the nodes obtained by other methods. DETAILED DESCRIPTION

[0046] Example 1: Figure 1-Figure 2 As shown, a complex network node influence ranking method based on structural entropy, the method comprising:

[0047] Step 1: Build a social network graph based on the data set, use two-dimensional structural entropy to discover communities, and obtain stable overlapping communities, so that each node and community is in a stable state, and ensure that each network node belongs to one or more communities;

[0048] Furthermore, the Step 1 includes:

[0049] Step 1.1. Select a dataset containing social network data, including nodes and the relationships (edges) between nodes, use the social network data to build a graph structure, use the network analysis library NetworkX to create a graph, and add nodes and edges to the graph;

[0050] Step 1.2, use the community discovery algorithm based on two-dimensional structural entropy to obtain multiple overlapping communities. When the two-dimensional structural entropy of each community remains stable, keep the existing structure of the community, calculate the two-dimensional structural entropy of each community and the two-dimensional structural entropy of the entire network, obtain the adjacent community matrix of the target node, and obtain a stable overlapping community.

[0051] Step 2: Calculate the influence of the node within the community and the influence of the node across communities, and perform a linear combination of the influence of the node within the community and the influence of the node across communities to obtain the comprehensive influence value of each node; the influence of the node consists of two parts, one is the influence of the node within the community, and the other is the influence of the node across communities. The influence within the community is the change in the structural entropy of the community after the node leaves the community, and the cross-community influence is the sum of the changes in the structural entropy of all target communities after the node joins the target community;

[0052] Furthermore, the Step 2 includes:

[0053] Step 2.1. Calculate the two-dimensional structural entropy of each community and obtain the adjacent community matrix of the target node. When the node is moved from the existing community to the target community, the volume and number of boundary edges of the original community are g respectively. in and v in , and then after the node leaves the original community, the community volume and the number of community border edges after the node leaves the community are g in ' and v in ', the influence of the node in the community after leaving the community is ΔSE in ;

[0054] g in '=g in +d-2n in (1)

[0055] v in '=v in +d (2)

[0056]

[0057] where d is the number of edges that the node is connected to; n in represents the number of neighbors of the node in the current or target community, that is, the number of connections between the node and other nodes in the community; vol is the volume of the entire graph, that is, the sum of the degrees of all nodes in the graph;

[0058] Step 2.2: According to the node's adjacent community matrix, the node target community matrix is ​​traversed in turn. For the target community, the volume and number of boundary edges of the community before the node joins are g and g respectively. cross and vcross , the community volume and the number of community border edges after the node joins the target community are g cross ' and v cross ', after updating the volume and number of boundary edges of the community, the node moves from the current community to the target community or becomes a community on its own. For each node after the move, the influence of the node across communities is calculated, which is ΔSE cross ;

[0059] g cross '=g cross -d+2n in (4)

[0060] v cross '=v cross -d (5)

[0061]

[0062] Step 2.3: Take the weighted sum of the influence of the node within the community and the influence of the node across communities to obtain the comprehensive influence of node i;

[0063] The influence of a node is composed of its influence within the community and its influence across communities. However, the proportions of the two are not necessarily equal. A network influence factor α is selected to balance the weights of the two, and the comprehensive influence of node i is obtained as follows:

[0064]

[0065] ΔSE in Represents the influence of the node in the community, that is, the authority of the node in the community; ΔSE cross Represents the influence of the node across communities. The node has influence not only in its own community, but also in other communities. adj_div represents the set of all other target communities.

[0066] Step 2.4: According to the IC propagation model, set α∈[0,1] with a step size of 0.01, and traverse the network influence factor α in turn to obtain the final number of nodes after propagation through the IC propagation model. Determine the network influence factor α with the largest number of propagated nodes on multiple data sets, thereby determining the proportion of influence within the community and cross-community influence on node influence, and then execute Step 2.3.

[0067] Step 3: Sort all nodes according to their comprehensive influence values ​​and identify the key nodes with the greatest influence in the social network.

[0068] Furthermore, the Step 3 includes:

[0069] Step 3.1. After obtaining the comprehensive influence of each node in the community according to the network influence factor, sort the nodes in the social network according to the comprehensive influence of the nodes. The greater the influence of the node, the more important the node is in the social network. When maximizing the influence, the higher the ranking of the node, the stronger its communication ability. Finally, the comprehensive influence ranking result of each node is obtained; the sorted node list is:

[0070] V sorted =SORT desc (V,key=INF(i)) (8)

[0071] Among them, V sorted It is a sorted list of nodes, in which the nodes are arranged in descending order of comprehensive influence; SORT desc is a sorting function, which means sorting the nodes in descending order; V is a set or list containing all nodes, and is also a parameter in the key sorting function, which means sorting the nodes according to the INF value. The node list is the collection of all nodes in the social network. Through the sorting operation, the nodes in the node list are arranged from high to low according to their comprehensive influence, forming a sorted list, that is, V sorted .

[0072] The present invention also provides a system for ranking the influence of complex network nodes based on structural entropy, the system comprising:

[0073] Overlapping community module, used to construct a social network graph based on the data set, use two-dimensional structural entropy to discover communities, obtain stable overlapping communities, make each node and community in a stable state, and ensure that each network node belongs to one or more communities;

[0074] The node influence module is used to calculate the influence of the node within the community and the influence of the node across communities, and to linearly combine the influence of the node within the community and the influence of the node across communities to obtain the comprehensive influence value of each node; the influence of the node consists of two parts, one is the influence of the node within the community, and the other is the influence of the node across communities. The influence within the community is the change in the structural entropy of the community after the node leaves the community, and the cross-community influence is the sum of the changes in the structural entropy of all target communities after the node joins the target community;

[0075] The sorting algorithm module is used to sort all nodes according to the comprehensive influence value and identify the key nodes with the greatest influence in the social network.

[0076] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned method for ranking the influence of complex network nodes based on structural entropy when executing the program.

[0077] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the method for ranking the influence of complex network nodes based on structural entropy is implemented.

[0078] The present invention also provides a computer program product, including a computer program, which, when executed by a processor, implements the above-mentioned complex network node influence ranking method based on structural entropy.

[0079] After obtaining the influence ranking results of each node in the network, we select the top 10 nodes or the top 20 nodes for comparison. We also use the selected nodes as the initial node set and simulate the propagation process through the IC propagation model to obtain the final number of affected nodes.

[0080] In order to illustrate the effect of the present invention, three groups of comparative experiments were set up. The first group of experiments verified the consistency of the nodes selected by the method of ranking the influence of nodes based on two-dimensional structural entropy and the nodes selected by other methods. The second group of experiments verified the effectiveness of the influential nodes selected by the method of ranking the influence of nodes based on two-dimensional structural entropy in the IC propagation model. The last group of experiments verified the importance of the nodes selected by the method of ranking the influence of nodes based on two-dimensional structural entropy in the entire network.

[0081] (1) The consistency between the nodes selected by the method of ranking the influence of nodes based on two-dimensional structural entropy and the nodes selected by other methods;

[0082] Compared with other methods of selecting influential nodes in social networks, we selected the first 10 nodes in the dataset and looked at the common nodes and independent nodes of the first 10 nodes selected by different methods. For easy observation, we displayed them on the Venn diagram. Figure 2 As shown in Figure 2, we selected the top 10 nodes of the Facebook social network and CA-GrQc social network datasets.

[0083] analyze Figure 2 It can be seen that the top 10 nodes ranked by influence obtained by the method of the present invention are mostly the same as the nodes obtained by other methods. Figure 2 In (a), in the Facebook network, among the top 10 nodes obtained by our method, 7 nodes overlap with other methods, and among the nodes obtained by other methods, at most 7 nodes overlap with methods different from their own. Figure 2 In the CA-GrQc network in (b), the first 10 nodes obtained by the method of the present invention based on influence are all recognized by other methods. LE method and DC method have 9 nodes overlapping with different methods. Compared with other methods, the nodes obtained by the method of the present invention are more consistent with the nodes obtained by other methods.

[0084] (2) The effectiveness of the influential nodes selected by the method of ranking the influence of nodes based on two-dimensional structural entropy in the IC propagation model;

[0085] The second group of experiments verified the effectiveness of the influential nodes selected by the method of ranking the influence of nodes based on two-dimensional structural entropy in the IC propagation model. That is, compared with the number of activated nodes obtained by other methods after the influence nodes were propagated through the IC model, the more the number of activated nodes, the more influential the nodes selected by this method are. The experimental results are shown in Table 1:

[0086] Table 1 shows the effectiveness of different methods (number)

[0087]

[0088] From Table 1, we can see that the nodes selected by the method of the present invention propagate the number of nodes on different data sets. Among them, on the data sets email, CA-GrQc, LastFMAsia, nethepht, and Epinions, the nodes selected by the method of the present invention have the largest number of final activated nodes after being simulated by the IC propagation model. On the Facebook data set, the nodes obtained by the DC method have the largest number of final activated nodes after being simulated by the IC propagation model, which is 11 nodes more than the number of nodes obtained by the method of the present invention. However, on the other 5 data sets, the number of final activated nodes we obtained is more than that of other methods. Therefore, the final number of activated nodes can verify the effectiveness of the influential nodes selected by the method of the present invention in the IC propagation model.

[0089] (3) The importance of nodes in the entire network is determined by ranking the influence of nodes based on two-dimensional structural entropy;

[0090] The third group of experiments verified the importance of nodes selected by the method of ranking nodes by influence based on two-dimensional structural entropy in the entire network. This group of experiments used the ratio of network efficiency decline to evaluate the influence of each node in the social network, selected a certain proportion of high-influence nodes to simulate network attacks, and observed the changes in network connectivity by removing these nodes and their related edges. By comparing the ratio of network efficiency decline before and after the attack, the importance of the attacked node in the network can be quantified. A significant decline in network efficiency indicates that the node has a critical influence. The experimental results are shown in Table 2.

[0091] Table 2 shows the network degradation ratio (%) of different methods

[0092]

[0093] From the analysis of Table 2, it can be seen that the network decline ratio of the method of the present invention is higher than that of all other methods when the node removal ratio is 2%, 3%, 5%, 6%, 7%, 8%, 9%, and 10%, indicating that the method of the present invention calculates the influence of the node by integrating the local attributes of the node and the global attributes of the social network, and sorts the nodes accordingly. In the experiment, the present invention examines the influence of each node in the social network by evaluating the ratio of network efficiency decline. The results show that the selected node has a significant impact on the connectivity of the entire network. The greater the ratio of network efficiency decline, the more important the selected node is to the network. Therefore, it can be proved that the node influence ranking method based on two-dimensional structural entropy of the present invention can effectively identify nodes that play a key role in the network.

[0094] Through the above experimental data, the present invention confirms the superiority of the node influence ranking method based on two-dimensional structural entropy in selecting effective nodes. Compared with the traditional method, the present invention not only considers the local information of the node, but also integrates the global information of the social network, thereby effectively supplementing the overall information omission problem caused by relying only on local information. In addition, the present method significantly improves the speed of processing nodes in large-scale networks and reduces the computational complexity. By comparing the number of common nodes of different methods, the consistency of the nodes selected by the method of ranking the influence of nodes based on two-dimensional structural entropy and the nodes selected by other methods is verified; according to the number of final activated nodes of the nodes obtained by different methods after the IC propagation model, the effectiveness of the influential nodes selected by the method of ranking the influence of nodes based on two-dimensional structural entropy in the IC propagation model is proved; finally, the important nodes in the attack network are simulated on the data set, which illustrates the importance of the nodes selected by the method of ranking the influence of nodes based on two-dimensional structural entropy in the entire network. The present invention proposes an influence ranking method that comprehensively considers local and global attributes. The method defines the influence of nodes by the influence of nodes within the community and the influence across communities and sorts the nodes by importance, which effectively overcomes the limitations of previous methods. Therefore, this method is not only innovative in theory, but also shows extremely high practical value in practical applications, especially in the fields of network structure analysis, information diffusion prediction and network security.

[0095] The specific implementation modes of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above implementation modes, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A complex network node influence ranking method based on structural entropy, characterized by: The method comprises: Step 1: Construct a social network graph based on the data set, use two-dimensional structural entropy to discover communities, and obtain stable overlapping communities; Step 2: Calculate the influence of the node within the community and the influence of the node across communities, and perform a linear combination of the influence of the node within the community and the influence of the node across communities to obtain the comprehensive influence value of each node; Step 3: Sort all nodes according to their comprehensive influence values ​​and identify the key nodes with the greatest influence in the social network.

2. According to claim 1, a complex network node influence ranking method based on structural entropy is characterized by: The Step 1 includes: Step 1.

1. Select a dataset containing social network data, use the social network data to build a graph structure, use the network analysis library NetworkX to create a graph, and add nodes and edges to the graph; Step 1.2: Use a community discovery algorithm based on two-dimensional structural entropy to obtain multiple overlapping communities. When the two-dimensional structural entropy of each community remains stable, the existing structure of the community is maintained to obtain stable overlapping communities.

3. According to claim 1, a complex network node influence ranking method based on structural entropy is characterized by: The Step 2 includes: Step 2.

1. Calculate the two-dimensional structural entropy of each community and obtain the adjacent community matrix of the target node. When the node is moved from the existing community to the target community, the volume and number of boundary edges of the original community are g respectively. in and v in , and then after the node leaves the original community, the community volume and the number of community border edges after the node leaves the community are g in ' and v in ', the influence of the node in the community after leaving the community is ΔSE in ; <h2 style=";text-align:left;direction:ltr">g<h2 style=";text-align:left;direction:ltr"> in <h2 style=";text-align:left;direction:ltr"> '=g<h2 style=";text-align:left;direction:ltr"> in <h2 style=";text-align:left;direction:ltr"> +D-2n<h2 style=";text-align:left;direction:ltr"> in <h2 style=";text-align:left;direction:ltr"> (1) v in '=v in +d (2) Where d is the number of edges the node is connected to, and n in represents the number of neighbors of the node in the current or target community, and vol is the volume of the entire graph; Step 2.2: According to the node's adjacent community matrix, the node target community matrix is ​​traversed in turn. For the target community, the volume and number of boundary edges of the community before the node joins are g and g respectively. cross and v cross , the community volume and the number of community border edges after the node joins the target community are g cross ' and v cross ', the node moves from the current community to the target community or becomes a separate community. For each node after the move, the influence of the node across communities is calculated, which is ΔSE cross ; <h2 style=";text-align:left;direction:ltr">g<h2 style=";text-align:left;direction:ltr"> cross <h2 style=";text-align:left;direction:ltr"> '=g<h2 style=";text-align:left;direction:ltr"> cross <h2 style=";text-align:left;direction:ltr"> -d+2n<h2 style=";text-align:left;direction:ltr"> in <h2 style=";text-align:left;direction:ltr"> (4) v cross '=v cross -d (5) Step 2.3: Take the weighted sum of the influence of the node within the community and the influence of the node across communities to obtain the comprehensive influence of node i; Select a network influence factor α to balance the weights of the two, and get the comprehensive influence of node i as: ΔSE in Represents the influence of the node in the community, ΔSE cross represents the influence of the node across communities, and adj_div represents the set of all other target communities; Step 2.4: According to the IC propagation model, the network influence factor α is traversed in turn to obtain the final number of nodes after propagation through the IC propagation model, and the network influence factor α with the largest number of propagated nodes on multiple data sets is determined. In this way, the proportion of influence within the community and influence across communities on the node influence is determined, and then Step 2.3 is executed.

4. According to claim 1, a complex network node influence ranking method based on structural entropy is characterized by: The Step 3 includes: After obtaining the comprehensive influence of each node in the community according to the network influence factor, the nodes in the social network are sorted according to the comprehensive influence of the nodes to obtain the comprehensive influence ranking results of each node; the sorted node list is: V sorted =SORT desc (V,key=INF(i)) (8) Where V sorted is the sorted node list, SORT desc is a sorting function, V is a set or list containing all nodes, key is a parameter in the sorting function, which means to sort the nodes according to the INF value.

5. A system for ranking the influence of complex network nodes based on structural entropy, characterized in that: The system comprises: a module for executing the method according to any one of claims 1-4.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, a complex network node influence ranking method based on structural entropy is implemented as described in any one of claims 1 to 4.

7. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, a complex network node influence ranking method based on structural entropy is implemented as described in any one of claims 1 to 4.

8. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, a complex network node influence ranking method based on structural entropy is implemented as described in any one of claims 1 to 4.

Images