Onset of small-world behavior in topologically evolving networks

Abstract

We evolve the topology of a network of N fully-coupled nodes that interact according to repulsion-attraction dynamics within a confining wall. The dynamics portrays each node's tendency to keep distance from its competitors while maintaining a lighter tendency to resist relative isolation. Each node is characterized by two parameters: an intrinsic mobility μ and a preferred neighboring distance ρ. Onset of clustering is found to occur at a critical variance in mobility, σ_μ² = 1, and in preferred neighboring distance, σ_ρ² = 10. This result implies that small-world behavior manifested in clustering can be triggered by the diversity of node population.