Universal dependence of distances on nodes degrees in complex networks

摘要

We have studied dependence of distances on node degrees between vertices of Erd s-Rényi random graphs, scale-free Barabási-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks. We have observed that the mean distance between two nodes of degrees ki and kj equals to = A – Blog(kikj). A simple heuristic theory for this scaling law is presented. Corrections due to the network clustering coefficient and node degree-degree correlations are taken into account.