Node Degree Distribution in Affiliation Graphs for Social Network Density Modeling

Abstract

The purpose of this article is to link high density in social networks with their underlying bipartite affiliation structure. Density is represented by an average number of a node’s neighbors (i.e. node degree or node rank). It is calculated by dividing a number of edges in a graph by a number of vertices. We compare an average node degree in real-life affiliation networks to an average node degree in social networks obtained by projecting an affiliation network onto a user modality. We have found recently that the asymptotic Newmann’s explicit formula relating node degree distributions in an affiliation network to the density of a projected graph overestimates the latter value for real-life datasets. We have also observed that this property can be attributed to the local tree-like structure assumption. In this article we propose a procedure to estimate the density of a projected graph by means of a mixture of an exponential and a power-law distributions. We show that our method gives better density estimates than the classic formula.