A network similarity evaluation method based on network motifs

Abstract

The present invention discloses a network similarity evaluation method based on network motifs. The method of the present invention includes two parts: data collection and preprocessing, and calculating network structure similarity. The data collection and preprocessing part includes four subtasks: constructing a network, an adjacency matrix, a node's neighbor set, and a network node motif distribution matrix, which provide a data basis for the subsequent calculation of the structural similarity between networks. The part for calculating the network structure similarity includes two subtasks: calculating the dispersion between network nodes and calculating the network structural similarity value, and finally obtaining the difference in structural properties between networks. The present invention considers the global importance of nodes at the macro level, and the topological structure of local networks at the micro level, and achieves a better balance between the local structure and the global structure of the network.

Description

Technical Field

[0001] The present invention belongs to the field of computer technology, and in particular relates to a network similarity evaluation method based on a network motif, which can evaluate the similarity of network structures according to the distribution of nodes based on the network motif. Background Art

[0002] The similarity of network structures is one of the important research directions in network science. This study aims to quantify the similarities and differences between different networks through the local to overall structure of the network. Its research is currently widely used in social sciences, economics, biology, computer science and other fields. Specifically, in the field of social networks, social relationships of related people can be classified; in the biological field, the comparison of the patient's cell network with the healthy cell network can help find a cure for the disease.

[0003] In recent years, with the rapid growth of available data in networks and the flexibility of network modeling, a large number of methods for network comparison have emerged. When analyzing complex networks on a structural basis, comparison methods using similarity (or dissimilarity) measures are crucial. Depending on the discipline, this problem is called graph matching, network comparison, or network alignment. Its essence is to study whether the sets of nodes in two graphs satisfy a one-to-one mapping relationship. It quantifies the differences between networks by comparing the structural topological differences of the networks, such as simpler topological structural features such as adjacency matrix and degree distribution, or more complex topological structural features such as network community structure and spectral entropy. Summary of the invention

[0004] The purpose of the present invention is to provide a network similarity evaluation method based on network motifs, which comprehensively considers the similarity of local and global structures of the network, and further verifies the reliability and applicability of the method.

[0005] The method of the present invention specifically comprises:

[0006] Step (1) data collection and preprocessing; including four subtasks: constructing a network, constructing an adjacency matrix, constructing a node's neighbor set, and constructing a network node motif distribution matrix; the details are as follows:

[0007] (1-1) Network construction: First, the network G = (V, E) is constructed based on the affiliation relationship between nodes and edges. The node set V = {v 1 ,v 2 ,…,v N},v n is the nth node in the network, n=1,2,…,N, N represents the number of nodes, and E represents the edge set.

[0008] (1-2) Construct the adjacency matrix: Construct the adjacency matrix A according to the affiliation between nodes and edges N×N; Specifically, when node v i and node v j When there is a connecting edge, A i,j The value of is 1, otherwise it is 0, i=1,2,…,N, j=1,2,…,N, i≠j.

[0009] (1-3) Construct the neighbor set T of the node = {t 1 ,t 2 ,…,t N}, where t n Represents node v n The set of neighbors.

[0010] (1-4) Constructing a network node motif distribution matrix: First, define a network motif as a connected, non-isomorphic subgraph consisting of 3 to 5 nodes in the network, and there are 30 different types of motifs in total; thus, construct a complete network node motif distribution matrix U = {U 1 (k),U 2 (k),U 3 (k),…,U N (k)},U i (k) is the node v i And the probability that the neighbor nodes constitute a k-type motif, U i (k) is a 1×30 dimensional vector.

[0011] Step (2) calculates the network structure similarity; it includes two subtasks: calculating the dispersion between network nodes and the network structural similarity value.

[0012] (2-1) Calculate the dispersion between network nodes: measure the heterogeneity of the network and capture the relevant characteristics of the network by measuring the similarity of the distribution of network motifs;

[0013] Measuring the Similarity of Network Motif Distribution in, represents the Jensen-Shannon divergence of the distribution of N nodes, The average value of node distribution

[0014] When NND(G) is maximum, it means that the heterogeneity of node connectivity in the network is maximum, and when NND(G) is minimum, it means that the node connections in the network are more uniform.

[0015] (2-2) Calculate the network structural similarity value; the network structural similarity value of network G and network G'

[0016] The network structural similarity value is composed of two parts and is adjusted by two weight parameters α and β, 0<α<1, 0<β<1. The larger the network structural similarity value between two networks, the smaller the structural similarity between the two networks, and vice versa.

[0017] In order to effectively compare network differences, the motifs in the network of the present invention method describe the pairwise interaction patterns between a fixed number of connected nodes. Compared with the structure based on "binary relationships" in traditional networks, network motifs can better analyze and capture the high-order structure between nodes, thereby making up for the defect that existing network structure similarity methods cannot capture global structural properties. The present invention describes the distribution of nodes in complex networks based on network motifs to obtain structural similarity values ​​between different networks. The present invention achieves an effective balance between the effectiveness, interpretability and computational efficiency of the results.

[0018] At the macro level, the method of the present invention considers the global importance of nodes through the motif-based distribution of nodes on the entire network; at the micro level, the topological structure of the local network, namely the heterogeneity of node connectivity, is considered, thereby achieving a better balance between the local structure and the global structure of the network, and finally defining the similarity value between two different network structures. DETAILED DESCRIPTION

[0019] The present invention will be further described below in conjunction with the technical solution, but the following examples are by no means limiting the present invention in any way.

[0020] A network similarity assessment method based on network motifs is performed in the following steps:

[0021] Step (1) Network construction: First, the network G = (V, E) is constructed based on the affiliation relationship between nodes and edges. The node set V = {v 1 ,v 2 ,…,v N},v n is the nth node in the network, n=1,2,…,N, N represents the number of nodes, and E represents the edge set.

[0022] Step (2) Construct the adjacency matrix: Construct the adjacency matrix A according to the affiliation between nodes and edges. N×N ; Specifically, when node v i and node v j When there is a connecting edge, A i,j The value of is 1, otherwise it is 0, i=1,2,…,N, j=1,2,…,N, i≠j.

[0023] Step (3) Construct the neighbor set T of the node 1 ,t 2 ,…,t N}, where tn Represents node v n The set of neighbors.

[0024] Step (4) Constructing a network node motif distribution matrix: First, define a network motif as a connected, non-isomorphic subgraph consisting of 3 to 5 nodes in the network, and there are 30 different types of motifs in total; thereby constructing a complete network node motif distribution matrix U = {U 1 (k),U 2 (k),U 3 (k),…,U N (k)},U i (k) is the node v i And the probability that the neighbor nodes constitute a k-type motif, U i (k) is a 1×30 dimensional vector.

[0025] Step (5) calculates the dispersion between network nodes: measures the heterogeneity of the network and captures the relevant characteristics of the network by measuring the similarity of the network motif distribution.

[0026] Measuring the Similarity of Network Motif Distribution in, represents the Jensen-Shannon divergence of the distribution of N nodes, The average value of node distribution

[0027] When NND(G) is maximum, it means that the heterogeneity of node connectivity in the network is maximum, and when NND(G) is minimum, it means that the node connections in the network are more uniform.

[0028] Step (6) Calculate the network structural similarity value; the network structural similarity value of network G and network G'

[0029] The network structural similarity value consists of two parts and is adjusted by two weight parameters α and β, 0<α<1, 0<β<1. The average connectivity between nodes is taken into account, that is, the motif-based distribution of nodes in the network; the second term The heterogeneity between nodes, i.e., the local structural differences in the network, is taken into account.

[0030] The greater the network structural similarity value between two networks, the smaller the structural similarity between the two networks, and vice versa.

Claims

1. A network similarity evaluation method based on network motifs, characterized in that: The method is specifically: Step (1) data collection and preprocessing; including constructing a network, constructing an adjacency matrix, constructing a node's neighbor set, and constructing a network node motif distribution matrix; specifically as follows: (1-1) Network construction: First, the network G = (V, E) is constructed based on the affiliation relationship between nodes and edges. The node set V = {v1, v2, …, v N },v n is the nth node in the network, n=1,2,…,N, N represents the number of nodes, E represents the edge set; (1-2) Construct the adjacency matrix: Construct the adjacency matrix A according to the affiliation between nodes and edges N×N ; Specifically, when node v i and node v j When there is a connecting edge, A i,j The value of is 1, otherwise it is 0, i=1,2,…,N, j=1,2,…,N, i≠j; (1-3) Construct the neighbor set T of the node = {t1, t2, …, t N }, where t n Represents node v n The set of neighbors of ; (1-4) Constructing the network node motif distribution matrix: First, define the network motif as a connected, non-isomorphic subgraph consisting of 3 to 5 nodes in the network, and there are 30 different types of motifs in total; thus, construct a complete network node motif distribution matrix U = {U1(k), U2(k), U3(k), …, U N (k)},U i (k) is the node v i And the probability that the neighbor nodes constitute a k-type motif, U i (k) is a 1×30 dimensional vector; Step (2) calculating the network structure similarity; Including calculating the dispersion between network nodes and the network structural similarity value; (2-1) Calculate the dispersion between network nodes: measure the heterogeneity of the network and capture the relevant characteristics of the network by measuring the similarity of the distribution of network motifs; Measuring the Similarity of Network Motif Distribution in, represents the Jensen-Shannon divergence of the distribution of N nodes, The average value of node distribution When NND(G) is maximum, it indicates that the heterogeneity of node connectivity in the network is the greatest, and when NND(G) is minimum, it indicates that the nodes in the network are more evenly connected; (2-2) Calculate the network structural similarity value; The network structural similarity value of network G and network G' The network structural similarity value is composed of two parts and is adjusted by two weight parameters α and β, 0<α<1, 0<β<1; the larger the network structural similarity value between the two networks, the smaller the structural similarity between the two networks, and vice versa.

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