Research on Shortest Paths-Based Entropy of Weighted Complex Networks

In order to provide a new measure for the structural characteristics of complex networks, a new shortest paths-based entropy (SPE) is proposed to describe the influence of degree and shortest path on network characteristics in this paper. The novel measurement based on shortest paths of node pairs and weights of edges. Many different approaches to measuring the complexity of networks have been developed. Most existing measurements unable to apply in weighted network that consider only one characteristic of complex networks such as degree or betweenness centrality. To some extent, the shortest paths-based entropy overcome the inadequacies of other network entropy descriptors. The method combines node degrees with shortest paths. For the purpose of proving the reasonableness of this method, we carry on a contrast analysis of the SPEs of different type networks, including: ER random network, BA scale-free network, WS small-world network and grid network. The results show that shortest paths-based entropy of complex networks is meaningful to evaluation of networks.