Local preferential attachment model for hierarchical networks

Abstract

In real-life networks, incomers may only connect to a few others in a local area for their limited information, and individuals in a local area are likely to have close relations. Accordingly, we propose a local preferential attachment model. Here, a local-area-network stands for a node and all its neighbors, and the new nodes perform nonlinear preferential attachment, π ( k i ) ∝ k i α , in local areas. The stable degree distribution and clustering-degree correlations are analytically obtained. With the increasing of α , the clustering coefficient increases, while assortativity decreases from positive to negative. In addition, by adjusting the parameter α , the model can generate different kinds of degree distribution, from exponential to power-law. The hierarchical organization, independent of α , is the most significant character of this model.