Community network key node identification method based on binomial entropy and van der Waals force between neighborhood nodes

Abstract

The invention belongs to the technical field of networks, and particularly relates to a community network key node identification method based on binomial entropy and van der Waals force between neighborhood nodes. Comprising the following steps: S1, processing a community network to obtain a binomial entropy of nodes in the community network; s2, the binomial entropy is corrected through a ReLU activation function; s3, calculating the overlap ratio of first-order neighbor nodes of the node to be tested on the topological structure of the community network; s4, solving Van der Waals forces of nodes in the community network; s5, processing results calculated in the steps S2-S4 through a linear normalization formula to obtain three index values; and S6, summing the three index values to obtain a node importance evaluation value in the community network, and finally realizing identification of the community network key nodes. According to the method, the problem that the original sorting is too coarse is solved, the time complexity is reduced, the node evaluation accuracy is improved, the efficiency can be ensured to a certain extent, and the importance degree of the nodes in the network is fully mined.

Description

Technical Field

[0001] The invention belongs to the field of network technology, and in particular relates to a method for identifying key nodes in a community network based on binomial entropy and van der Waals forces between neighborhood nodes. Background Art

[0002] With the advent of the big data era, the scale and structure of networks have become larger and more complex, and the existing key node identification methods need to be optimized to meet the identification needs of large-scale networks. Complex networks abstract entities in real networks into nodes, and abstract the relationships between entities into edges, and reflect the complex systems of the real world through the network structure composed of nodes and edges. By identifying key nodes, in the social field, the formation and evolution laws of social relations can be better derived, providing an important basis for the in-depth understanding of social relations; in the military field, the key links and weaknesses in operations can be determined to provide support for the formulation of more scientific and reasonable combat strategies; in the economic field, the key links and bottlenecks in economic development can be determined to provide support for the formulation of more scientific and reasonable economic policies. Therefore, the research on key nodes of complex networks has attracted widespread attention at home and abroad. If the functions of key nodes are damaged or fail, it will lead to the collapse of the network or the loss of function. Therefore, the study of important nodes in complex networks plays a vital role in the stability and efficiency of the network.

[0003] In order to verify the applicability and accuracy of the present invention, the algorithm is applied to different types of basic networks and compared with existing advanced algorithms to evaluate the effectiveness of the algorithm in actual networks. For example, Guo Chengyuan et al. proposed a node importance ranking algorithm based on iterative K-shell and improved information entropy, which mainly uses the information entropy proposed by Shannon to further improve the precision of the algorithm. In complex networks, the higher the node information entropy, the more information the node receives, and the coarse-grained network sorting is optimized; Zou Long et al. proposed a network important node identification method based on degree joint information entropy, which reflects the importance of the node through the degree values ​​of the current node and the neighboring nodes. The proportion of node information is called the trust between nodes, and the node neighborhood overlap is considered to further evaluate whether the same assigned nodes contribute the same importance to the entire network; Lin Xin et al. proposed a node degree and neighborhood overlap label propagation algorithm, which measures the importance of nodes by calculating the neighborhood network similarity and the node degree value, thereby optimizing the order between nodes.

[0004] In summary, the existing mainstream methods have certain limitations in application and there is room for improvement:

[0005] 1. Although the method of reflecting the global network through the local network does not need to traverse the entire network to obtain global information, thus avoiding the problem of high time complexity, the research based on unweighted undirected networks is less practical and lacks consideration of the complexity and diversity of node attributes.

[0006] 2. Although the idea of ​​uniting neighboring node degrees is introduced to describe the relationship between nodes, it only considers the relationship between nodes within the second-order range, and lacks description of the nodes to be tested and the higher-order range.

[0007] Based on this, a new method for identifying key nodes in complex networks is designed to solve the problem that the original sorting is too coarse-grained. At the same time, it optimizes the accuracy and timeliness of identifying key nodes in complex networks by quantifying the contribution of neighbor nodes to the importance of the current node and combining the impact of topological structure on importance. Summary of the invention

[0008] In view of the difficulties faced by the key node identification problem and the shortcomings of the existing methods, the main innovation of the present invention is in the algorithm design idea. A key node identification method based on binomial entropy and van der Waals forces between neighboring nodes (binomial entropy and van der Waals forces between linkage similarity, EVL) is proposed. The method combines information entropy and neighborhood overlap to solve the problem that the original sorting is too coarse-grained. The concept of information entropy is introduced to quantify the contribution of surrounding nodes to the importance of the current node. The neighborhood overlap is used to highlight the influence of topological structure on importance. The sorting result has a significant improvement on the basic method. In measuring the importance of nodes in the network, the binomial entropy with lower complexity is used, and the nodes are preprocessed in combination with the activation function to reduce the time complexity; in describing the relationship between nodes, the domain similarity method is improved and the van der Waals force measurement method is introduced. The position of the node in the network is comprehensively considered, and the influence of the node and the topological information are used to take into account the triangle structure between nodes to reflect the importance of the node. This not only ensures the improvement of the accuracy of node evaluation, but also guarantees efficiency to a certain extent, and fully explores the importance of the node in the network.

[0009] In order to achieve the above technical effects, the present invention proposes a method for identifying key nodes in a community network based on binomial entropy and van der Waals forces between neighboring nodes, comprising:

[0010] S1: Process the community network to obtain the binomial entropy of the nodes in the community network;

[0011] S2: The binomial entropy of S1 is modified by the ReLU activation function;

[0012] S3: Calculate the overlap of the first-order neighbor nodes of the node to be tested in the community network topology structure based on the neighborhood overlap evaluation formula;

[0013] S4: Map the nodes in the community network to molecules or atoms, solve the van der Waals forces of the nodes in the community network, and characterize the influence of the nodes in the community network;

[0014] S5: The results calculated by S2-S4 are respectively mapped to the interval [0,1] through the linear normalization formula;

[0015] S6: Sum the three indicator values ​​of S5 to obtain the node importance evaluation value in the community network, sort the importance of the community network nodes according to the node importance evaluation value, and finally realize the identification of key nodes in the community network.

[0016] Preferably, the binomial entropy E of node i in the S1 community network i It is expressed as:

[0017] E i =-[p i log2p i +(1-p i )log2(1-p i )]

[0018] Among them, p i is the probability set required for node entropy in the community network based on node degree, p i Defined as:

[0019]

[0020] Among them, k i and k j represents the node degree of community network nodes i and j, Γ i represents the first-order neighbors of node i in the community network.

[0021] Preferably, S2 is specifically:

[0022] Through the ReLU activation function, the threshold interval of the binomial entropy of the nodes in the community network is set to (3, ∞). Nodes with binomial entropy less than 3 are not subject to subsequent calculations, thereby correcting the importance level of nodes in the community network. The formula of the ReLU activation function is:

[0023]

[0024] Preferably, S3 is specifically:

[0025] The neighborhood overlap evaluation formula is:

[0026]

[0027] Among them, LS represents the overlap of the first-order neighbor nodes of the community network node to be tested in the community network topology structure, N(i) represents the set of first-order neighbor nodes of community network node i, and the overlap

[0028] represents the number of all adjacent node pairs of community network node i; sim(i,j) represents the neighborhood overlap between community network node i and community network node j; It is the difference in the overlap between community network node i and community network node j.

[0029] Preferably, S4 is specifically:

[0030] Map the nodes in the community network to molecules or atoms, and express the degree of the node as the van der Waals constant of the molecule or atom. The influence of the node in the community network is proportional to the number of neighbor nodes and inversely proportional to the shortest path distance. Therefore, the van der Waals force of the node in the community network is:

[0031]

[0032] Among them, i represents a node in the community network, and the degree value is k i , j represents a non-i node, and its degree value is k j , d ij represents the shortest path length between community network node i and community network node j; It is the directional attraction generated between community network nodes. is the instantaneous dipole attraction between community network nodes.

[0033] Preferably, the linear normalization formula of S5 is:

[0034]

[0035] in, and E i The minimum and maximum values ​​in the data, x V(i)min and x V(i)max are the minimum and maximum values ​​in V(i) data, respectively, and x LSmin and x LSmin are the minimum and maximum values ​​in the LS data respectively. By using the linear normalization formula, x i The values ​​of (i=1, 2, 3) are scaled to [0, 1] so that after normalization 0 < x i <1.

[0036] Preferably, the summation formula of the three index values ​​of S6 is:

[0037]

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] The present invention proposes a key node identification method based on binomial entropy and van der Waals forces between link similarity (EVL), combines information entropy and neighborhood overlap method on the basis of basic method to solve the problem of original sorting being too coarse-grained, introduces the concept of information entropy to quantify the contribution of surrounding nodes to the importance of current node, highlights the influence of topological structure on importance through neighborhood overlap, and the sorting result is greatly improved on the basis of basic method. Binomial entropy with low complexity is used to measure the importance of nodes in the network, and the nodes are preprocessed in combination with activation function to reduce time complexity; in describing the relationship between nodes, the domain similarity method is improved and the van der Waals force measurement method is introduced, the position of the node in the network is comprehensively considered, and the influence of the node and the triangular structure between the nodes are used to reflect the importance of the node by taking into account the topological information, so that not only the accuracy of node evaluation is improved, but also the efficiency can be guaranteed to a certain extent, and the importance of the node in the network is fully explored. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0041] In the attached picture:

[0042] Figure 1 The schematic diagram of the process structure of the method of the present invention is shown;

[0043] Figure 2 It is shown that the present invention reduces the time complexity by using the distribution of node entropy for data preprocessing;

[0044] Figure 3 The present invention is used to identify nodes and disintegrate networks in sparse networks;

[0045] Figure 4 The present invention is used to illustrate node identification and network collapse in a high-density community network;

[0046] Figure 5 The present invention illustrates node identification and network collapse in a peer-to-peer distributed decentralized network;

[0047] Figure 6 The present invention is shown for node identification and network collapse in a large-scale network. DETAILED DESCRIPTION

[0048] The following is combined with Figure 1 -Attached Figure 6 The preferred embodiments of the present invention are described. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0049] The key node identification problem in complex networks refers to determining the most influential nodes in the network. In the study of complex networks, these nodes have an important impact on the stability and overall structure of the network. The undirected and unweighted complex network model can be expressed as G = (V, E), where V = (v1, v2, v3…v N ) is a set of network nodes, v1, v2, v3…v N Indicates that the network contains N nodes, E = (e1, e2, e3…e s ) is the set of edges between nodes, e1,e2,e3…e s It means there are s edges in the network, N = |V| is the total number of nodes in the network, and S = |E| is the total number of edges in the network.

[0050] A method for identifying key nodes in a community network based on binomial entropy and van der Waals forces between neighboring nodes, comprising:

[0051] S1: Process the community network to obtain the binomial entropy of the nodes in the community network. Specifically:

[0052] The process of entropy construction first needs to consider the probability set p required to construct the entropy based on node degree. i , entropy can be used to quantify the uncertainty and complexity of the network structure. In general, a characteristic parameter in the network structure is used to reduce the computational time cost. i As a parameter, node degree refers to the number of other nodes directly connected to a node in the network. Each edge connected to the node is counted as the node's degree. The node degree is the number of edges connected to the node. Therefore, define p i is the set of probabilities required for the community network node entropy based on node degree:

[0053]

[0054] Among them, k i and k j represents the node degree of community network nodes i and j, Γ i Represents the first-order neighbors of node i in the community network. First-order neighbors refer to other nodes that are directly connected to a specific node (or vertex).

[0055] Information entropy is used to measure the amount of information in an event. If X is a set of possible events x1, x2, …, x m, x1, x2, …, x m The number of events represented, p i is the probability required to calculate the information entropy of node i, then the entropy of event X can be calculated according to the following formula.

[0056]

[0057] The larger the entropy value, the more information can be transmitted. In this invention, each time the node entropy is detected, the node to be detected is event X, and all other nodes are event To realize the binomial distribution feature, the concept of binomial entropy is introduced to measure the importance of nodes. Binomial entropy can focus on key binary decisions in complex networks and ignore other unimportant variables, thereby highlighting the most important nodes. According to the definition of Shannon information, the entropy of binomial distribution (in nat units) is defined as follows:

[0058] Assume random variable X~B(n,p), that is Then the mathematical expectation E(x)=np, and the variance D(x)=np(1-p).

[0059]

[0060] prove:

[0061]

[0062] Similarly, we can get:

[0063]

[0064] Therefore, we can get:

[0065]

[0066] Where n is the number of independent trials in the binomial distribution, p is the probability of success, k is the number of successful trials, and p(x=k) represents the probability of k successes out of n trials. n! is the factorial of n, k! is the factorial of k, (nk)! is the factorial of (nk), represents the probability of getting exactly k successes in n trials, p k represents the probability of each of k successes occurring, (1-p) n-k Indicates n- k The probability of each failure occurring.

[0067] According to the above formula, the present invention defines the binomial entropy E of node i in the community network as i It is expressed as:

[0068] E i =-[p i log2p i+(1-p i )log2(1-p i )]

[0069] S2: The binomial entropy of S1 is modified by the ReLU activation function. Specifically:

[0070] Nodes whose binomial entropy calculated by S1 is less than 3 will not enter the subsequent calculation. Nodes whose binomial entropy is greater than 3 will calculate the corresponding neighborhood overlap and van der Waals force. As the network scale becomes larger and larger, more nodes need to be processed. In order to reduce the time complexity of the algorithm, the nodes are preprocessed by binomial entropy.

[0071] pass Figure 2 Data analysis, through the ReLU activation function, the threshold interval of the binomial entropy of the nodes in the community network is set to (3, ∞), and the nodes with binomial entropy less than 3 will not enter the next round of calculation, thereby realizing the correction of the importance level of the nodes in the community network.

[0072] Therefore, the ReLU activation function is proposed to solve the problem of gradient disappearance by filtering the above node entropy with the help of the linear rectification function ReLU (RectifiedLinearUnit). The gradient of ReLU can only take two values: 0 or 1. When the input is less than 0, the gradient is 0; when the input is greater than 0, the gradient is 1. The advantage is that the multiplication of the gradient of ReLU will not converge to 0, and the result of the multiplication can only take two values: 0 or 1. If the value is 1, the gradient keeps the value unchanged for forward propagation; if the value is 0, the gradient stops forward propagation from this position. The importance level of nodes in the community network is further modified, that is, the binomial entropy of S1 is modified by the ReLU activation function. The formula of the ReLU activation function is:

[0073]

[0074] S3: Calculate the overlap of the first-order neighbor nodes of the node to be tested in the community network topology structure based on the neighborhood overlap evaluation formula; specifically:

[0075] The importance of a node in a network is not only related to the node itself, but also to the degree of dependence of the first-order neighbor nodes of the node on the node. By calculating the overlap of the first-order neighbor nodes of the node in the network topology, we can determine whether the node is easy to replace. The lower the overlap, the less likely the node is to be replaced. The node similarity index is defined as the Jaccard index value, which helps to understand the network structure and function. The formula is expressed as

[0076]

[0077] Among them, N(i) represents the set of first-order neighbor nodes of node i, |N(i)| represents the number of first-order neighbor nodes of node i, |N(i)∩N(j)| and |N(i)∪N(j)| represent the number of common neighbor nodes and the total number of neighbor nodes of nodes i and j respectively. The value of sim(i,j) is between 0 and 1. When sim(i,j)=1, it means that nodes i and j have exactly the same neighbors, that is, their neighborhoods completely overlap; when sim(i,j)=0, it means that they do not have any common neighbors. On the basis of the LLS algorithm, the relationship between the degree and the edge between nodes is considered, and the neighborhood overlap evaluation formula LS is optimized to be:

[0078]

[0079] Among them, LS represents the overlap of the first-order neighbor nodes of the community network node to be tested in the community network topology structure, N(i) represents the set of first-order neighbor nodes of community network node i, and the overlap is a combinatorial mathematical formula that represents the number of all adjacent node pairs of node i in the community network; because the degree value of each node i is k, there are k adjacent nodes with node i. i There are k edges i -1 adjacent node, total There are node pairs, but because they appear in pairs, they are divided by 2. sim(i,j) represents the neighborhood overlap between community network node i and community network node j, which measures the similarity of the adjacent node sets of the two nodes. is the difference in the overlap between community network node i and community network node j. A larger value means that the adjacent nodes are less similar in function or topology, which means that the nodes are less likely to be replaced. Conversely, it means that the two sets have more common edges in the network.

[0080] S4: Map the nodes in the community network into molecules or atoms, solve the van der Waals force of the nodes in the community network, and characterize the influence of the nodes in the community network; specifically: inspired by the gravitational model that uses node gravity to characterize the importance of nodes, and considering that the van der Waals force can measure the size of the intermolecular force, this paper introduces the van der Waals force into the complex network, maps the nodes in the network into molecules or atoms, and uses the van der Waals force of the nodes to characterize the influence of the nodes, that is, the importance.

[0081] Van der Waals force refers to the force between molecules. In complex networks, van der Waals force is introduced into complex networks, nodes in the network are mapped to molecules or atoms, and the degree of the node is expressed as the van der Waals constant of the molecule or atom. Since the van der Waals force between nodes has the characteristics of both attraction and repulsion, the evaluation accuracy of the node is improved. The basic idea of ​​the node importance evaluation algorithm based on van der Waals force is to comprehensively consider the relative position of the node in the network and the influence of its neighboring nodes.

[0082] Therefore, the present invention maps the nodes in the community network to molecules or atoms, and represents the degree of the node as the van der Waals constant of the molecule or atom. The van der Waals force is a weak force that is ubiquitous between molecules. Its characteristic is that it contains both attractive and repulsive forces. Specifically, the degree of the node (i.e., the number of directly connected neighboring nodes) is regarded as a manifestation of the van der Waals constant of the molecule or atom. This mapping is not only intuitive, but also cleverly uses the degree as the basic indicator of the local importance of the node. Furthermore, based on the characteristics of the van der Waals force, the algorithm is designed to assume that the influence of the node is proportional to the number of its neighboring nodes (similar to the attractive part of the van der Waals force), and inversely proportional to the shortest path distance between these neighboring nodes (similar to the performance of the repulsive force in the van der Waals force at close distances).

[0083] Therefore, the influence of a node in a community network is proportional to the number of neighboring nodes and inversely proportional to the shortest path distance. Therefore, the van der Waals force of a node in a community network is:

[0084]

[0085] Among them, i represents a node in the community network, and the degree value is k i , j represents a non-i node, and its degree value is k j , d ij represents the shortest path length between community network node i and community network node j; It is the directional attraction between community network nodes, which mainly expresses the repulsive effect when overlapping. This force is related to the distance d ij The relationship of inverse proportionality to the 12th power is closer; is the instantaneous dipole attraction between community network nodes. This force is more inversely proportional to the sixth power of the distance. The force between two nodes is inversely proportional to the distance between them. The van der Waals attraction is inversely proportional to So when the van der Waals force at the node is positive, it manifests as repulsion; otherwise, it manifests as attraction.

[0086] S5: To eliminate the influence of different dimensions and value ranges of the three different methods mentioned in S2, S3, and S4, and to facilitate the next step of index fusion, the three calculation results are mapped to the same interval using the normalization method. At the same time, the numerical fusion of the three algorithms needs to be considered in the subsequent calculation process. To unify the dimensions of different algorithms, the results of S2-S4 calculations are respectively mapped to the interval [0,1] through the linear normalization formula; the linear normalization formula is:

[0087]

[0088] in, and E i The minimum and maximum values ​​in the data, x V(i)min and x V(i)max are the minimum and maximum values ​​in V(i) data, respectively, and x LSmin and x LSmin are the minimum and maximum values ​​in the LS data respectively. By using the linear normalization formula, x i The values ​​of (i=1, 2, 3) are scaled to [0, 1] so that after normalization 0 < x i <1.

[0089] S6: Sum the three indicator values ​​of S5 to obtain the node importance evaluation value in the community network, sort the importance of the community network nodes according to the node importance evaluation value, and finally identify the key nodes of the community network. The formula for summing the three indicator values ​​is as follows to obtain the node importance evaluation value:

[0090]

[0091] Evaluation indicators

[0092] The importance of nodes is evaluated by selecting three indicators: network residual edges, network efficiency, and network sensitivity. Nodes are deleted in order of importance, and the impact of node deletion on network structure and function is obtained by analyzing the changes in the three indicators, thus reflecting the importance of nodes to the network.

[0093] 1 Network remaining edges

[0094] The remaining network edge represents the remaining network connectivity after a node is destroyed. When a node is deleted, the greater the damage to the network connectivity, the more important the node is. The calculation method is as follows:

[0095]

[0096] Among them, E is the total number of edges in the remaining network after each node removal, and M is the number of edges in the initial network.

[0097] 2. Network Efficiency

[0098] Networks with different functions have different characteristics. The connectivity scale of a network may not necessarily reflect the effectiveness of the network. Therefore, based on the global efficiency EF, we propose a method to evaluate the overall efficiency of a network group containing multiple subnetworks. Let the overall efficiency of the network be TE.

[0099]

[0100] Where, T i is a connected subgraph i, n i is the size (number of nodes) of the ith connected subgraph. If the node is isolated, the network service efficiency EF = 0. If the network efficiency curve decreases faster after deleting the node, the importance of the attacked node is higher. If the node is isolated, the network service efficiency EF = 0.

[0101] 3. Network sensitivity

[0102] In theory, deleting individual nodes is unlikely to completely destroy the network, but it will affect the stability of the network. From the perspective of network structure, the stability of the network can be reflected indirectly through the network sensitivity rate. The more important the attacked node is, the greater the fluctuation of the network will be, and the peak will appear first. The calculation is as follows

[0103]

[0104] Among them, n s is the number of components of size s, n is the number of network nodes, and σ is used to determine the threshold of remaining fragments after the network is destroyed. As network nodes are gradually removed, the network is decomposed into many small-sized network fragments. When the network disintegrates to a certain extent, a peak value of sensitivity S will appear on the image. The peak value also means that the original network has been disassembled into a group of fragments less than or equal to the threshold σ to the maximum extent.

[0105] Simulation experiment:

[0106] The simulation uses four real data sets, namely Bn-macaque-rhesus-brain, FB-pages-government, P2P-Gnutella25 and Road-Italy, to verify the effect of EVL algorithm on node importance evaluation. The algorithm performance is evaluated by combining three indicators: network residual edges, network efficiency and network sensitivity.

[0107] Table 1 Network parameters involved in the experiment

[0108] Dataset name Number of nodes Number of edges Average Average clustering coefficient Triple ratio Figure No. Bn-macaque-rhesus-brain 242 4.1k 12 53.26％ 36.15％ (a) FB-pages-government 7.1k 89.4k 25 41.09％ 22.38％ (b) P2P-Gnutella25 22.7k 54.7k 4 0.531％ 0.454％ (c) Road-Italy 6.7M 7M 2 0.102％ 0.269％ (d)

[0109] The four groups of figures (a), (b), (c), and (d) represent the four data sets selected in this paper. In order to make the experimental results have a certain universality, group (a) represents sparse networks, group (b) represents high-density community networks, group (c) represents peer-to-peer distributed decentralized networks, and group (d) represents large-scale networks.

[0110] The four curves in each figure of the experimental results represent the importance ranking of the nodes of the data set network using the CEKS, DE, LLS-LPA and EVL algorithms, and the most important nodes are deleted in order according to the order of each method. The network change curve is then drawn using three indicators: network residual connectivity, network service efficiency, and network sensitivity. The experimental results can not only evaluate the advantages and disadvantages of the algorithm in ranking important nodes, but also analyze the impact of network parameters on network robustness. It is not difficult to see from the experimental results that the algorithm in this paper has certain advantages in ranking important nodes in complex networks.

[0111] pass Figure 3-Figure 6 As shown, each group of left, middle and right figures represent the three indicators of network service efficiency, network residual connectivity and network sensitivity respectively. The horizontal axis is the percentage of deleted nodes to original nodes, and the vertical axis is the indicator capacity. The following conclusions can be drawn. In terms of network efficiency indicators, from the four groups of figures (left), it can be observed that the EVL algorithm is slightly inferior to the LLS-LPA algorithm when the nodes are first deleted, but the effect improves in a short time and is better than the other three algorithms, and it is the first to stabilize; in terms of network residual connectivity, the red curve represented by the EVL algorithm in the three groups of figures (middle) can intuitively see that the decline speed is faster than the other three methods; in terms of network sensitivity, in the three groups of figures (right), deleting nodes after sorting according to the EVL algorithm can cause the network to quickly produce large fluctuations and quickly reach a peak. From Figure 3-Figure 6 Overall, the EVL algorithm in this paper has a network order of magnitude of 10 3 The effect is excellent, but in large-scale networks, the advantage is not very obvious and there is still room for improvement. Overall, the node ranking algorithm in this paper can better reflect the importance of network nodes than the other three methods.

[0112] From the parameters of the four networks and Figure 3-Figure 6 The curve graph analyzes the impact of network parameters on the overall robustness of the network. When the proportion of triplets is high, it means that there is a high tendency of connection clustering between similar nodes in the network, which increases the network's ability to transmit information and enhances the network's resistance to attacks; and a higher average clustering coefficient often means a higher graph density, because the connection between clustered nodes increases the total number of connections in the network, which means that the network is more robust. According to the network parameters, the four groups of network triplets (a), (b), (c), and (d) and the average clustering coefficient are ranked in order (a)>(b)>(c)>(d). Combined with Figure 3-Figure 6From the four groups of curves, it can be seen that when the nodes of the four groups of networks are deleted, the network efficiency decreases to a stable state, and the node deletion ratios of the four groups of graphs (left) are (a)>(b)>(c)>(d); in terms of the network's residual connectivity, it can be clearly seen that the slopes of the four groups of graphs (middle) are (a)<(b)<(c)<(d) from low to high; when the network sensitivity reaches its peak, the node deletion ratios of the four groups of graphs (right) are (a)>(b)>(c)>(d). In summary, the proportion of triples and average clustering coefficients in network parameters plays a key role in the robustness of the network.

[0113] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for identifying key nodes in a community network based on binomial entropy and van der Waals forces between neighboring nodes, characterized in that: include: S1: Process the community network to obtain the binomial entropy of the nodes in the community network; S2: The binomial entropy of S1 is modified by the ReLU activation function; S3: Calculate the overlap of the first-order neighbor nodes of the node to be tested in the community network topology structure based on the neighborhood overlap evaluation formula; S4: Map the nodes in the community network to molecules or atoms, solve the van der Waals forces of the nodes in the community network, and characterize the influence of the nodes in the community network; S5: The results calculated by S2-S4 are respectively mapped to the interval [0,1] through the linear normalization formula; S6: Sum the three indicator values ​​of S5 to obtain the node importance evaluation value in the community network, sort the importance of the community network nodes according to the node importance evaluation value, and finally realize the identification of key nodes in the community network.

2. The key node identification method based on binomial entropy and van der Waals forces between neighboring nodes according to claim 1, characterized in that: Binomial entropy E of node i in S1 community network i It is expressed as: E i =-[p i log2p i +(1-p i )log2(1-p i )] Among them, p i is the probability set required for node entropy in the community network based on node degree, p i Defined as: Among them, k i and k j represents the node degree of community network nodes i and j, Γ i represents the first-order neighbors of node i in the community network.

3. The key node identification method based on binomial entropy and van der Waals forces between neighboring nodes according to claim 2, characterized in that: S2 is specifically: Through the ReLU activation function, the threshold interval of the binomial entropy of the nodes in the community network is set to (3, ∞). Nodes with binomial entropy less than 3 are not subject to subsequent calculations, thereby correcting the importance level of nodes in the community network. The formula of the ReLU activation function is:

4. The key node identification method based on binomial entropy and van der Waals forces between neighboring nodes according to claim 3, characterized in that: S3 is specifically: The neighborhood overlap evaluation formula is: Among them, LS represents the overlap of the first-order neighbor nodes of the community network node to be tested in the community network topology structure, N(i) represents the set of first-order neighbor nodes of community network node i, and the overlap represents the number of all adjacent node pairs of community network node i; sim(i,j) represents the neighborhood overlap between community network node i and community network node j; It is the difference in the overlap between community network node i and community network node j.

5. The key node identification method based on binomial entropy and van der Waals forces between neighboring nodes according to claim 4, characterized in that: S4 is specifically: Map the nodes in the community network to molecules or atoms, and express the degree of the node as the van der Waals constant of the molecule or atom. The influence of the node in the community network is proportional to the number of neighbor nodes and inversely proportional to the shortest path distance. Therefore, the van der Waals force of the node in the community network is: Among them, i represents a node in the community network, and the degree value is k i , j represents a non-i node, and its degree value is k j , d ij represents the shortest path length between community network node i and community network node j; It is the directional attraction generated between community network nodes. is the instantaneous dipole attraction between community network nodes.

6. The key node identification method based on binomial entropy and van der Waals forces between neighboring nodes according to claim 5, characterized in that: The linear normalization formula of S5 is: in, and E i The minimum and maximum values ​​in the data, x V(i)min and X V(i)max are the minimum and maximum values ​​in V(i) data, respectively, and x LSmin and x LSmin are the minimum and maximum values ​​in the LS data respectively. Through the linear normalization formula, x i The values ​​of (i=1, 2, 3) are scaled to [0, 1] so that after normalization 0 < x i <1.

7. The key node identification method based on binomial entropy and van der Waals forces between neighboring nodes according to claim 6, characterized in that: The formula for summing the three index values ​​of S6 is:

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