Effects of community structure on navigation

The dynamic behaviors of the complex network are crucially affected by its structural properties, which is an essential issue that has attracted much interest. In this paper, the effects of the community structure on the navigability of complex networks are comprehensively investigated. The networks we explored, each of which is embedded in a K -dimension Euclidean space based on a landmark based multi-dimensional scaling (LMDS) algorithm, are of scale-free configuration with tunable modularity, obtained by regulating the proportion of edges in and between communities. Pairs of source and target are selected from the nodes in the networks, and the messages are passed along from source to target in this space based on the greedy routing strategy. The extensive experiments we carried out suggest that, the higher navigability, defined by proportion of messages successfully delivered, is related to stronger modularity of the complex networks. In addition, the optimal dimension K of the embedding Euclidean space is found to be approximately identical to half of the landmark number.