Explanation of Correlation between Adjacent Vertices in Network Formed by Traces of Random Walkers

Abstract

We investigated certain kinds of vertex correlation in networks formed by traces of random walkers. In this paper, the sign of correlation between degree and local clustering on adjacent vertices is interpreted based on the capacity for new creation of links for highly connected vertices. These interpretations are consistent with numerical simulation of network evolution. Other types of correlation can be related with each other. It is interesting that the local rules of network evolution determined by the movement of random walkers naturally provide large clustering coefficients and various finite vertex correlations.