A community detection method based on core motif triangle

Abstract

The present invention discloses a community detection method based on core motif triangles, and relates to the technical field of community detection. Through the local relationship between nodes in the network, a core triangle motif is selected to represent the local topological structure of the node, and the core triangle motif is used as the basic unit for label diffusion. The core triangle drive is used to avoid the oscillation generated in the process of label propagation and the result of the algorithm falling into the local optimum, so as to produce a stable community detection result.

Description

Technical Field

[0001] The present invention mainly relates to the technical field of community detection in undirected and unweighted networks, and in particular to a community detection method based on core motif triangles. Background Art

[0002] In recent years, complex network analysis has been widely used in social networks, biological networks and other fields, and has become an important tool for understanding and analyzing complex systems. Traditional community detection methods mainly focus on network topology and identify community structures in the network by analyzing the connection relationship between nodes. However, such methods often ignore the core structure in the network, that is, the sub-network composed of closely connected and influential nodes.

[0003] The core structure of the network plays a vital role in maintaining network stability and promoting information dissemination. For example, in social networks, the core structure is usually composed of active users, who have an important influence on the dissemination of information and the formation of opinions; in biological networks, the core structure may represent key protein complexes or functional modules, which are essential for maintaining normal cell function. Therefore, how to combine the network topology and core structure to perform more accurate community division has become a research hotspot and difficulty in the current field of complex network analysis. Integrating core structure information into the community detection process can more accurately identify key nodes and communities in the network, reveal the organizational structure and functional mechanism of the network, and provide theoretical basis and technical support for network optimization, information dissemination control, disease diagnosis and treatment, etc. The present invention provides a local label diffusion algorithm based on the core triangle motif, which comprehensively considers the topological structure and core structure in the network to obtain better results and further improve the existing community detection algorithm. Summary of the invention

[0004] The purpose of the present invention is to provide a community detection method based on core motif triangle in order to solve the above problems.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] According to one aspect of the present invention, a community detection method based on a core motif triangle is provided for community detection in undirected and unweighted networks. The method is characterized in that: the motif driver of the core triangle composed of nodes is used to adjust the labels of the nodes inside the core triangle, and the local community detection algorithm is prone to fall into the local optimum and produce oscillations during the label propagation process, which affects the label allocation. The specific implementation steps are as follows:

[0007] A. Initialization of local information of complex networks

[0008] In a complex network G = (V, E), where V is the node set and E is the edge set, two nodes v i and v j The Jaccard similarity is defined as Equation 1.

[0009]

[0010] In formula 1, N vi Represented as node v i The neighbor nodes in Driven are marked as target nodes. For each target node v i The importance of all nodes in the complex network is calculated by formula 2, and all nodes are arranged in order from high to low in terms of local importance to obtain the sequence V n = {V i |NI(v1)≥...≥NI(v i )≥...≥NI(v n ),1≤i≤n},n=|V| is the number of network nodes, analyze each target node v i The local topology of each target node v i Use formula 3 to find the core triangle motif of each target node, as follows:

[0011]

[0012] In formula 2, similarity(V i ,V j ) represents the jaccard similarity between two nodes.

[0013] B. Initialization of local information of complex networks

[0014] According to the sequence {V n} Perform label diffusion and divide the core triangle motif of the target node into the following three cases:

[0015] (1) Homogeneous transfer: When the target node v i The label of the node is the same as the label of the adjacent node that forms the core triangle pattern. The nodes that form the core triangle motif belong to the same community and have close connections within the community, which makes the community structure more stable and obvious. At this time, the labels of the nodes in the core triangle motif are not updated, and the search for the next target node continues;

[0016] (2) Label attraction: When there is a node v jWhen the label of the target node is inconsistent with the label of the target node, the core triangle driven method uses the local importance between nodes to determine whether to pass the label of the target node to the point v j ; Since nodes with high local importance have closer relationships with their neighbors, they are more capable of spreading labels to neighboring nodes; therefore, when NI(v i )>NI(v j ), target node v i Propagate its label to node v j ; Otherwise, search for the next target node from {Vn} and continue label diffusion;

[0017] (3) Local expansion: If the target node v i If the node is different from the other two class labels, the node and the adjacent nodes may be used as boundary nodes between communities. At this time, the connection degree and close relationship between the node and different communities are calculated by formula 4. i Assign to the community with the maximum benefit function;

[0018] benefit(v i ,C x )=Connection(v i ,C x )+ Cohesion(v i ,C x ) Formula (4)

[0019] in, Represents all neighbor nodes of the core triangle formed by the target node, They represent the closeness between the node and the community Cx and the cohesion of the community Cx respectively;

[0020] C. Merger of associations

[0021] In the Driven algorithm, the merging method mainly focuses on the local topological structure between communities, and merges weak communities according to the triangular motif. Communities usually contain the following two characteristics:

[0022] (1) The community is structurally isolated from other communities, that is, it has few connections with other communities;

[0023] (2) The internal nodes of the community are structurally interconnected, that is, the internal connectivity of the community is large;

[0024] Among them, the Driven triangle motif defines weak communities to measure the cohesion within each community, as shown in Formula 5:

[0025]

[0026] For a Driven weak community Cx, find the community that is most closely connected to Cx. If the merged society Not a member of a weak society and If the number increases, the societies will be merged.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] The algorithm model in the present invention can be applied to reveal the local topological behavior of a real network, that is, to discover and analyze the community structure in the real network. In a complex real network, the community detection can be performed based on the core triangle motif of the network to complete the division of the community structure. In the social network that is most closely related to the Internet, the social network platform can establish a network information matrix based on the information uploaded by the user, according to various information such as age, gender, profession, hobbies, and usage time, and complete the division of different communities through the algorithm model in the present invention. It can usually be used for social software circle of friends analysis, career introduction analysis, friend discovery and other related functions. In other application fields, for example in biology, it can be used to analyze the complex food chain network structure, and can also be used for feature extraction and dimensionality reduction of complex protein networks to complete the division of different protein structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 This is a flow chart of the community detection algorithm driven by the core triangle motif of the present invention;

[0030] Figure 2 Schematic diagrams of the triangle motif of the present invention in different situations;

[0031] Figure 3 The karate dataset of the present invention;

[0032] Figure 4 The Polbooks dataset of the present invention;

[0033] Figure 5 It is the Football dataset of the present invention. DETAILED DESCRIPTION

[0034] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the present invention is further explained below in conjunction with specific implementation methods.

[0035] The core triangle motif driven community detection algorithm process of the technical solution of the present invention is as follows: Figure 1 As shown:

[0036] The network targeted by the present invention is an undirected and unweighted network, represented by G = (V, E), where V is the node set and E is the edge set. Where n = |V| is the number of network nodes, and m = |E| is the number of network edges. The specific implementation steps are as follows:

[0037] A. Initialization of local information of complex networks

[0038] In a complex network G = (V, E), two nodes v i and v j The Jaccard similarity is defined as Equation 1.

[0039]

[0040] In formula 1 Represented as node v i The neighbor nodes in Driven are marked as target nodes. For each target node v i The importance of all nodes in the complex network is calculated by formula 2, and all nodes are arranged in order from high to low local importance to obtain the sequence V n = {V i |NI(v1)≥...≥NI(v i )≥...≥NI(v n ),1≤i≤n}. Analyze each target node v i The local topology of each target node v i Use Formula 3 to find the core triangle motif of each target node.

[0041]

[0042] In formula 2, similarity(V i ,V j ) represents the jaccard similarity between two nodes.

[0043] B. Initialization of local information of complex networks

[0044] According to the sequence {V n} Perform label diffusion, and divide the core triangle motif of the target node into the following three cases, such as Figure 2 shown.

[0045] (1) Homogeneous transfer: When the target node v iThe label of the node is the same as the label of the adjacent node that forms the core triangle motif. The nodes that form the core triangle motif belong to the same community and have close connections within the community. This makes the community structure more stable and obvious. At this time, the labels of the nodes in the core triangle motif are not updated, and the search for the next target node continues;

[0046] (2) Label attraction: Figure 2 In (a), the red arrows indicate the attraction of a node to nodes with different labels, and the target node v i The label of a node v in its core triangle motif j Inconsistent, NI(v i ) and NI(v j ) represent the nodes v i and v j The local importance of NI(v i )>NI(v j ), target node v i Propagate its label to node v j Otherwise, label diffusion will continue by searching for the next target node from {Vn};

[0047] (3) Local expansion: If the target node v i If the node is different from the other two class labels, the node and the adjacent nodes may serve as boundary nodes between communities. At this time, the degree of connection and close relationship between the node and different communities are calculated by Formula 4, and the class label with the largest benefit function is selected as the label of the target node.

[0048] benefit(v i ,C x )=Connection(v i ,C x )+ Cohesion(v i ,C x ) Formula (4)

[0049] in, Represents all neighbor nodes of the core triangle formed by the target node, They represent the closeness between the node and the community Cx and the cohesion of the community Cx respectively;

[0050] C. Merger of associations

[0051] In the label diffusion stage, some nodes cannot form a triangle and therefore cannot participate in label diffusion. In addition, in the label diffusion stage, the presence of multiple important nodes in the same community may also cause the community to be divided into multiple small communities, so some initial communities need to be merged to form the final community.

[0052] Many methods use modularity metrics and the number of edges within a community to merge communities. The use of modularity has a contradiction: the largest modularity does not necessarily correspond to the best community detection results, and there is a certain deviation from the actual community structure. In addition, methods based on modularity tend to divide the entire network into groups of relatively equal size, resulting in "resolution limitation".

[0053] In addition, many methods assume that all edges within a community are equally important, while ignoring the local structure formed by these internal edges. The cohesion of a community depends not only on the number of internal edges, but also on the local structure between communities. In the Driven algorithm, the merging method proposed in this patent focuses on the local topological structure between communities and merges weak communities based on the triangular motif. Inspired by the traditional concept of community, communities usually contain the following two characteristics:

[0054] (1) The community is structurally isolated from the rest of the community (i.e., it has few connections with other communities);

[0055] (2) The internal nodes of the community are structurally interconnected (i.e., the internal connectivity of the community is high).

[0056] The Driven triangle motif defines weak communities to measure the cohesion within each community, as shown in Formula 5:

[0057]

[0058] For a Driven weak community Cx, find the community that is most closely connected to Cx. If the merged society Not a member of a weak society and If the number increases, the societies will be merged.

[0059] The algorithm model in the present invention can be applied to reveal the local topological behavior of a real network, that is, to discover and analyze the community structure in the real network. In a complex real network, the community detection can be performed based on the core triangle motif of the network to complete the division of the community structure. In the social network that is most closely related to the Internet, the social network platform can establish a network information matrix based on the information uploaded by the user, according to various information such as age, gender, profession, hobbies, and usage time, and complete the division of different communities through the algorithm model in the present invention. It can usually be used for social software circle of friends analysis, career introduction analysis, friend discovery and other related functions. In other application fields, for example in biology, it can be used to analyze the complex food chain network structure, and can also be used for feature extraction and dimensionality reduction of complex protein networks to complete the division of different protein structures.

[0060] Comparison of embodiments:

[0061] The present invention selects a real network community data set for verification, so as to analyze and verify the feasibility and accuracy of the algorithm. The present invention uses 13 real data sets: Karate, Polbooks, Football, Youtube and DBLP, etc. 13 open source data sets, mainly from (https: / / snap.stanford.edu / data / ). Among them, Karate, Polbooks and Football belong to small data sets (the number of nodes ranges from 34 to 115), Net-science, PowerGrid, etc. belong to medium-sized data sets (the number of nodes is about 1w nodes), Youtube, DBLP and Amazon belong to large data sets (the order of magnitude of ten thousand), and the data set introduction is shown in Table 1. In order to verify the effectiveness of the algorithm, the algorithm is compared with LSMD, LBLP, Leiden, ECES, LCDR, Infomap, LPA and Louvain, these eight comparison algorithms. In Tables 2, 3 and 4, the experimental results of the Driven ratio algorithm under different evaluation indicators are shown, and "-" in the table indicates that the experimental results are missing.

[0062] Table 1 Introduction to experimental datasets

[0063]

[0064]

[0065] Table 2 Quantitative comparison of modularity (Q) of CoreTirM algorithm and other comparison algorithms

[0066]

[0067] Table 3 NMI quantification comparison of CoreTirM algorithm and other comparison algorithms

[0068]

[0069] Table 4 F-measure quantitative comparison of CoreTirM algorithm and other comparison algorithms

[0070]

[0071] From the quantitative comparison of the experimental results in Table 2, Table 3 and Table 4, it can be seen that the evaluation indicators NMI, F-Measure and modularity of the label diffusion algorithm based on the core triangle of the present invention have the best comprehensive performance among the comparison algorithms. This is because the core triangle motif with high structural stability can more easily generate communities that better reflect the real network topology. Therefore, our Driven triangle motif is used to capture the close connections and high-order structures between nodes for label diffusion. When the label of a node is uncertain, the label is propagated from high-importance nodes to low-importance nodes according to the core triangle pattern. This is conducive to quickly building the initial community and avoiding label oscillation, thereby promoting algorithm convergence.

[0072] Figure 1 It is the main flow chart of the present invention. Figure 1 The whole algorithm process is divided into: label diffusion and community merging.

[0073] Figure 2 These are three cases of label diffusion based on core triangles in the present invention, where subgraph (a), subgraph (b) and subgraph (c) represent three different label diffusion strategies, respectively: homogeneous transmission, label attraction and local expansion.

[0074] Figure 3 , Figure 4 and Figure 5 The community detection results of three common real network data sets are represented respectively. The Driven algorithm proposed in the patent of this invention adopts the strategy of label diffusion using the core triangle motif, which can achieve ideal community division results.

[0075] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0076] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A community detection method based on core motif triangles for community detection in undirected and unweighted networks, characterized by: The core triangle motif composed of nodes is used as the driver to adjust the labels of the nodes inside the core triangle, so as to deal with the problem that the local community detection algorithm is prone to fall into the local optimum and produce oscillations during the label propagation process, which affects the label allocation. The specific implementation steps are as follows: A. Initialization of local information of complex networks In a complex network G = (V, E), where V is the node set and E is the edge set, two nodes v i and v j The Jaccard similarity is defined as formula 1; Formula (1) In formula 1 Represented as node v i The neighbor nodes in Driven are marked as target nodes. For each target node v i The importance of all nodes in the complex network is calculated by formula 2, and all nodes are arranged in order from high to low local importance to obtain the sequence ,n = |V| is the number of network nodes, analyze each target node v i The local topology of each target node v i Use formula 3 to find the core triangle motif of each target node, as follows: Formula (2) Formula (3) In formula 2, similarity(V i , V j ) represents the jaccard similarity between two nodes; B. According to the sequence {V n } Perform label diffusion and divide the core triangle motif of the target node into the following three cases: (1) Homogeneous transfer: When the target node v i The label of the node is the same as the label of the adjacent node that forms the core triangle pattern. The nodes that form the core triangle motif belong to the same community and have close connections within the community, which makes the community structure more stable and obvious. At this time, the labels of the nodes in the core triangle motif are not updated, and the search for the next target node continues; (2) Label attraction: When there is a node v j When the label of the target node is inconsistent with the label of the target node, the core triangle driven method uses the local importance between nodes to determine whether to pass the label of the target node to the point v j ; Since nodes with high local importance have closer relationships with their neighbors, they are more capable of spreading labels to neighboring nodes; therefore, when NI(v i )>NI(v j ), target node v i Propagate its label to node v j ; Otherwise, search for the next target node from {Vn} and continue label diffusion; (3) Local expansion: If the target node v i If the node is different from the other two class labels, the node and the adjacent nodes may be the boundary nodes between communities. At this time, the connection degree and close relationship between the node and different communities are calculated by formula 4, and the class label with the largest benefit function is selected as the label of the target node; Formula (4) in, Represents all neighbor nodes of the core triangle formed by the target node, , Respectively represent the closeness between the node and the community Cx and the community C x cohesion; C. Merger of associations In the Driven algorithm, the merging method mainly focuses on the local topological structure between communities, and merges weak communities according to the triangular motif. Communities usually contain the following two characteristics: (1) The community is structurally isolated from other communities, that is, it has few connections with other communities; (2) The internal nodes of the community are structurally interconnected, that is, the internal connectivity of the community is large; Among them, the Driven triangle motif defines weak communities to measure the cohesion within each community, as shown in Formula 5: Formula (5) For a Driven weak community Cx, find the community that is most closely connected to Cx, and calculate the internal If the merged society Not a member of a weak society and If the number increases, the societies will be merged.

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