Node Similarity Measure in Directed Weighted Complex Network Based on Node Nearest Neighbor Local Network Relative Weighted Entropy

Node similarity is a significant basis for analyzing features in complex network. For complex network with directed weighted edge, the complexity of the relationship among nodes and the diversity of relationship weights make measure node similarity complicated from the huge amounts of nodes. Therefore, a novel node similarity measure is proposed based on the design of node nearest neighbor local network relative weighted entropy. Firstly, degree and strength based directed weighted complex network model is constructed, on the basis of that, the Node Nearest Neighbor Local network is defined. The structural features of each node in the local network are quantized into a set of decision probabilities with multiple indicators. Furthermore, Node Connection Tightness is given to compute the influence of structural complex relationship in local network on node similarity. And then, to evaluate how the outward & inward degree and strength of nodes in the local network affect node similarity, the concept of Node Nearest Neighbor Local Network Relative Weighted Entropy is designed to define Node Relative Difference for measuring the structural difference between any two nodes. Accordingly, a novel node similarity measure is designed to measure the similarity between any pair of nodes in directed weighted complex network, and then the Similar Node Mining Algorithm is proposed to obtain most similar nodes. To clarify the availability and effectiveness of the proposed measure, two sets of experiments were conducted on real-world complex networks. The results show that the measure can not only mine nodes with the most similarity in the same module, but also mine the most similarity nodes from different modules.