Arbitrary degree distribution and high clustering in networks of locally interacting agents

Abstract

Many real world networks, such as social networks, are primarily formed through local interactions between agents. Additionally, in contrast with common network models, social and biological networks exhibit a high degree of clustering. Here we construct a class of network growth models based on local interactions on a metric space, capable of producing arbitrary degree distributions as well as a naturally high degree of clustering akin to biological networks. As a specific example, we study the case of random- walking agents, though most results hold for any linear stochastic dynamics. Agents form bonds when they meet at designated locations we refer to as "rendezvous points." The spatial distribution of the rendezvous points determines key characteristics of the network such as the degree distribution. For any arbitrary (monotonic) degree distribution, we are able to analytically solve for the required rendezvous point distribution.