On generating power-law networks with assortative mixing

Power-law networks are often used to model a wide range of real-world networks such as social networks, technological networks, and biological networks. Assortative mixing, or assortativity, is a tendency for similar-degree nodes to connect to each other. It is known that a positive degree of assortativity is present in social networks whereas a negative degree is present in technological networks. Both of these networks display the power-law degree property. It is thus important to have a network construction model that can generate power-law networks with different degrees of assortativity. Existing construction models are based on node degree information to determine how nodes are connected in the network. In this paper, we investigate a new model based on our hypothesis that each node has a singular "fitness" value representing its attractiveness to other nodes and that the network's growth is influenced by node fitness rather than node degree. The proposed model is a growth model without any re-wiring; the network is formed by adding a new node or a link between two nodes at each time step. Our theoretical findings are substantiated by a simulation study.