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 , in local areas. The stable degree distribution and clusteringdegree 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.
For example REF investigate a local preferential attachment model to generate hierarchical networks with tunable degree distribution, ranging from exponential to power-law.
Local preferential attachment model for hierarchical networks
Physica A-statistical Mechanics and Its Applications
Mathematics