Fitness-Weighted Preferential Attachment with Varying Number of New Connections

Preferential attachment models are used to explain the emergence of power laws in the degree distributions of networks. These models assume that a new node attaches to a network by establishing edges to a fixed number of nodes. Nonetheless, for many empirical networks the number of new edges varies as more nodes become part of the network. This paper extends the linear preferential attachment model by considering that the number of new edges is characterized by a random variable that obeys a power law probability function. While most new nodes connect to a few nodes, some nodes connect to a larger number. We characterize the dynamics of growth of the degrees of the nodes and the degree distribution of the network.