A two-hop neighbor preference-based random network graph model with high clustering coefficient for modeling real-world complex networks

Abstract

The Erdos-Renyi (ER) random network model generates graphs under the assumption that there could exist a link u-v between two nodes u and v irrespective of whether or not the two nodes had a common neighbor before the establishment of the link. As a result, random network graphs generated under the ER model 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 the node degrees, and hence could not match closely to graphs abstracting real-world networks. In this paper, we propose a random network graph model that gives preference to closing the triangle involving three nodes u, w and v with existing links u-w and w-v (i.e., node v is strictly a two-hop neighbor of node u). 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: matching closely to several real-world network graphs that are commonly studied for complex network analysis.