Network evolution by nonlinear preferential rewiring of edges

The mathematical framework for small-world networks proposed in a seminal paper by Watts and Strogatz sparked a widespread interest in modeling complex networks in the past decade. However, most of research contributing to static models is in contrast to real-world dynamic networks, such as social and biological networks, which are characterized by rearrangements of connections among agents. In this paper, we study dynamic networks evolved by nonlinear preferential rewiring of edges. The total numbers of vertices and edges of the network are conserved, but edges are continuously rewired according to the nonlinear preference. Assuming power-law kernels with exponents αα and ββ, the network structures in stationary states display a distinct behavior, depending only on ββ. For β>1β>1, the network is highly heterogeneous with the emergence of starlike structures. For β<1β<1, the network is widely homogeneous with a typical connectivity. At β=1β=1, the network is scale free with an exponential cutoff.

► We study networks evolved by nonlinear preferential rewiring of edges.
► We assumed the power-law kernels with exponents αα and ββ to model the probabilities of a vertex losing or gaining a new edge.
► We find that the network structure in the stationary states depends only on the exponent ββ, while αα can be arbitrary.
► The network is highly heterogeneous for β>1β>1 or widely homogeneous for β<1β<1.
► In the critical case marking the transition between these two regimes, β=1β=1, the network is scale free in general.