Local preferential attachment model for hierarchical networks

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(ki)∝kiα, in local areas. The stable degree distribution and clustering-degree correlations are analytically obtained. With the increasing of αα, the clustering coefficient increases, while assortativity decreases from positive to negative. In addition, by adjusting the parameter αα, the model can generate different kinds of degree distribution, from exponential to power-law. The hierarchical organization, independent of αα, is the most significant character of this model.