Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment rule using time-dependent data. Model networks are grown...

Scale-free networks are characterized by a degree distribution with power-law behavior. Although scale-free networks have been shown to arise in many areas, ranging from the World Wide Web to transportation or social networks, degree distributions of other observed networks often differ from the...

The network properties of a graph ensemble subject to the constraints imposed by the expected degree sequence are studied. It is found that the linear preferential attachment is a fundamental rule, as it keeps the maximal entropy in sparse growing networks. This provides theoretical evidence in...

The cluster-degree of a vertex is the number of connections among the neighbors of this vertex. In this paper we study the cluster-degree of the generalized Barabási–Albert model (GBA model) whose exponent of degree distribution ranges from 2 to ∞. We present the mean-field rate equation...