Efficiency of informational transfer in regular and complex networks

TL;DR

This paper introduces a new measure of local efficiency in complex networks, revealing that declustered small-world networks are highly efficient despite low clustering, and applies this to transportation systems.

Contribution

It proposes a modified efficiency measure for local analysis and applies it to declustered, small-world, and weighted networks, including real transportation systems.

Findings

Declustered small-world networks are locally efficient despite low clustering.

Unweighted small-world and scale-free networks are both globally and locally efficient.

Weighted networks like subway systems exhibit high efficiency, providing insights into transportation network performance.

Abstract

We analyze the process of informational exchange through complex networks by measuring network efficiencies. Aiming to study non-clustered systems, we propose a modification of this measure on the local level. We apply this method to an extension of the class of small-worlds that includes {\it declustered} networks, and show that they are locally quite efficient, although their clustering coefficient is practically zero. Unweighted systems with small-world and scale-free topologies are shown to be both globally and locally efficient. Our method is also applied to characterize weighted networks. In particular we examine the properties of underground transportation systems of Madrid and Barcelona and reinterpret the results obtained for the Boston subway network.