Network Information Flow in Small World Networks

TL;DR

This paper investigates the information flow capacity of small-world networks, providing bounds and revealing that random rewiring typically does not affect their capacity, highlighting fundamental communication limits.

Contribution

It offers the first bounds on the capacity of small-world networks and shows that random rewiring does not significantly change their communication capacity.

Findings

Upper and lower bounds for small-world network capacity

Random rewiring does not alter network capacity with high probability

Insights into fundamental communication limits in small-world topologies

Abstract

Recent results from statistical physics show that large classes of complex networks, both man-made and of natural origin, are characterized by high clustering properties yet strikingly short path lengths between pairs of nodes. This class of networks are said to have a small-world topology. In the context of communication networks, navigable small-world topologies, i.e. those which admit efficient distributed routing algorithms, are deemed particularly effective, for example in resource discovery tasks and peer-to-peer applications. Breaking with the traditional approach to small-world topologies that privileges graph parameters pertaining to connectivity, and intrigued by the fundamental limits of communication in networks that exploit this type of topology, we investigate the capacity of these networks from the perspective of network information flow. Our contribution includes upper and lower bounds for the capacity of standard and navigable small-world models, and the somewhat surprising result that, with high probability, random rewiring does not alter the capacity of a small-world network.