Expansion and Search in Networks

TL;DR

This paper investigates the expansion properties of real-world networks, introduces a new measure called the expansion signature, and demonstrates how high expansion facilitates efficient decentralized search, outperforming traditional methods.

Contribution

It introduces the concept of expansion signatures for real-world networks and links these properties to improved decentralized search strategies.

Findings

High expansion correlates with efficient searchability.

Standard graph measures do not fully explain searchability.

Expansion-based search outperforms traditional methods.

Abstract

Borrowing from concepts in expander graphs, we study the expansion properties of real-world, complex networks (e.g. social networks, unstructured peer-to-peer or P2P networks) and the extent to which these properties can be exploited to understand and address the problem of decentralized search. We first produce samples that concisely capture the overall expansion properties of an entire network, which we collectively refer to as the expansion signature. Using these signatures, we find a correspondence between the magnitude of maximum expansion and the extent to which a network can be efficiently searched. We further find evidence that standard graph-theoretic measures, such as average path length, fail to fully explain the level of "searchability" or ease of information diffusion and dissemination in a network. Finally, we demonstrate that this high expansion can be leveraged to facilitate decentralized search in networks and show that an expansion-based search strategy outperforms typical search methods.