Influence of reciprocal edges on degree distribution and degree correlations

Abstract

Reciprocal edges represent the lowest-order cycle possible to find in directed graphs without self-loops. Representing also a measure of feedback between vertices, it is interesting to understand how reciprocal edges influence other properties of complex networks. In this paper, we focus on the influence of reciprocal edges on vertex degree distribution and degree correlations. We show that there is a fundamental difference between properties observed on the static network compared to the properties of networks, which are obtained by simple evolution mechanism driven by reciprocity. We also present a way to statistically infer the portion of reciprocal edges, which can be explained as a consequence of feedback process on the static network. In the rest of the paper, the influence of reciprocal edges on a model of growing network is also presented. It is shown that our model of growing network nicely interpolates between Barabási-Albert (BA) model for undirected and the BA model for directed networks.