A Random Network Model with High Clustering Coefficient and Variation in Node Degree

Abstract

The Erdos-Renyi model-based random network graphs are characteristic of having a low clustering coefficient (a measure of the probability for a link to exist between any two neighbors of a node) and low variation in node degrees, and hence do not match closely to graphs abstracting real-world networks. Our hypothesis is that the clustering coefficient of the nodes could increase if preference is given to closing as many triangles as possible during link formation. Accordingly, when node u is looking for a new link to be setup with some other node x, we consider x along with the two-hop neighbors of u and choose one among these nodes with a probability plink as the new neighbor of node u. The proposed Two-Hop Neighbor Preference (THNP)-based model generates random graphs whose clustering coefficient decreases with increase in node degree, but still exhibits a Poisson-style distribution for node degree and path length.