Smallest small-world network

TL;DR

This paper identifies the most efficient small-world network structure as having a single central node with uniformly distributed shortcuts, supported by theoretical analysis and genetic algorithm simulations.

Contribution

It characterizes the optimal small-world network structure with a single center, advancing understanding of network efficiency design.

Findings

Single-center small-world networks are most efficient.

Networks with multiple centers are nearly as efficient.

Genetic algorithms support the theoretical results.

Abstract

Efficiency in passage times is an important issue in designing networks, such as transportation or computer networks. The small-world networks have structures that yield high efficiency, while keeping the network highly clustered. We show that among all networks with the small-world structure, the most efficient ones have a single ``center'', from which all shortcuts are connected to uniformly distributed nodes over the network. The networks with several centers and a connected subnetwork of shortcuts are shown to be ``almost'' as efficient. Genetic-algorithm simulations further support our results.