Research On Nodes Similarity In Complex Networks And Their Application

In fact, almost all complex systems can be abstracted as networks which are composed of nodes and edges. As a powerful tool, complex network science can help us to study complex systems commodiously and thoroughly. Analyzing similarities between elements in complex systems is a core issue in many fields of science, nodes similarity is the precondition for discovering actual information from complex networks, and it is of great significance for us to research similarities both on theory and reality aspects. This paper focuses on the definition and application of nodes similarity in complex networks and the mainwork are as follow:Considering the shortcomingsof traditional similarity indices, a novel cosine similarity index based on nodes distance is proposed. The main idea of this index is using vectors to represent network nodes and the cosine distances between vectors are similarities between nodes.On community detection in complex networks, three new community detection algorithms are proposed based on nodes cosine similarity index which include algorithm based on core nodes, spectral clustering algorithm and hierarchical clustering algorithm. This community detection algorithm based on core nodes is selecting nodes with larger degree as core nodes, and utilizing core nodes to absorb other nodes based on cosine similarities between them to detect communities; The main idea of spectral bisection algorithm is transforming cosine similarity matrix into a matrix with the same character as Laplacian matrix of network. Then two communities can be detected by the second-smallest eigenvector of the transformed matrix;The hierarchical clustering algorithm utilizes cosine similarity to detect communities. Normalized mutual information(NMI) is used as criterion for division of hierarchical tree. Experiment results demonstrate the feasibility of this algorithm.On the problem of link prediction in complex networks, three new nodes similarity indices including CD, CDI and LD are proposed. Experiment results demonstrate that CD and CDI indices can effectively overcome influence of low clustering coefficient of networks. What's more, CD and CDI indices are appropriate for link prediction in positive assortative coefficient and negative assortative coefficient networks respectively. LD index based on nodes cosine similarity can effectively improve prediction accuracy of traditional link prediction algorithms.