Structure of complex networks: Quantifying edge-to-edge relations by failure-induced flow redistribution
File(s)1303.6241v3.pdf (2.35 MB)
Accepted version
Author(s)
Schaub, MT
Lehmann, J
Yaliraki, SN
Barahona, M
Type
Journal Article
Abstract
The analysis of complex networks has so far revolved mainly around the role of nodes and communities of nodes. However, the dynamics of interconnected systems is commonly focalised on edge processes, and a dual edge-centric perspective can often prove more natural. Here we present graph-theoretical measures to quantify edge-to-edge relations inspired by the notion of flow redistribution induced by edge failures. Our measures, which are related to the pseudo-inverse of the Laplacian of the network, are global and reveal the dynamical interplay between the edges of a network, including potentially non-local interactions. Our framework also allows us to define the embeddedness of an edge, a measure of how strongly an edge features in the weighted cuts of the network. We showcase the general applicability of our edge-centric framework through analyses of the Iberian Power grid, traffic flow in road networks, and the C. elegans neuronal network.
Date Issued
2014-04-30
Online Publication Date
2013-03-25
2014-10-14T11:30:53Z
Journal / Book Title
Network Science, 2014, 2(1), pp. 66--89
Copyright Statement
© Cambridge University Press 2014. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press. Network Science: http://journals.cambridge.org/action/displayJournal?jid=NWS
Source Database
crossref
Description
14.10.14 KB. Ok to add accepted version to spiral
Identifier
http://dx.doi.org/10.1017/nws.2014.4
http://arxiv.org/abs/1303.6241v3
Notes
24 pages, 6 figures
Publisher URL