The degree distribution in random intersection graphs

Abstract

We study the degree distribution in a general random intersection graph introduced by Godehardt and Jaworski (Exploratory Data Analysis in Empirical Research, pp. 68-81, Springer, Berlin, 2002). The model has shown to be useful in many applications, in particular in the analysis of the structure of data sets. Recently Bloznelis (Lithuanian Math J 48:38-45, 2008) and independently Deijfen and Kets (Eng Inform Sci 23:661-674, 2009) proved that in many cases the degree distribution in the model follows a power law. We present an enhancement of the result proved by Bloznelis. We are able to strengthen the result by omitting the assumption on the size of the feature set. The new result is of considerable importance, since it shows that a random intersection graph can be used not only as a model of scale free networks, but also as a model of a more important class of networks - complex networks. © 2012 Springer-Verlag Berlin Heidelberg.