Network Rewiring Dynamics to Form Clustered Strategic Networks

Abstract

Burt’s Structural Hole Theory provides a theoretical foundation for individuals in a network to strategically seek a position in the network that gives them advantages by connecting them with a diverse range of others in different social cliques. Kleinberg et al. in [10] proposed an algorithm for the best response dynamics for the individuals in a network when they act strategically to maximize the number of structural holes in their neighbourhood during the formation of links. In this paper, we demonstrate through a set of experiments that networks that emerge at equilbria of strategic games such as the one proposed in [10], do not have characteristics of real-world networks. This leads us to follow an approach of studying the capacity of a network to hold maximum number of structural holes while maintaining it’s properties such as degree distribution and clustering coefficient. We also propose a new payoff utility function and a stochastic dynamic rewiring process with modified pairwise stability. Carrying out a set of experiments on real-world and synthetically generated networks, we empirically examine the number of structural holes that can be maintained in a network with realistic characteristics. We demonstrate that our payoff utility is able to maintain the clustering coefficient in a degree preserving rewiring scheme.