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Structure of complex networks: Quantifying edge-to-edge relations by failure-induced flow redistribution

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Title: Structure of complex networks: Quantifying edge-to-edge relations by failure-induced flow redistribution
Authors: Schaub, MT
Lehmann, J
Yaliraki, SN
Barahona, M
Item 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.
Issue Date: 30-Apr-2014
URI: http://hdl.handle.net/10044/1/17834
DOI: http://dx.doi.org/10.1017/nws.2014.4
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
Notes: 24 pages, 6 figures
Publisher URL: http://dx.doi.org/10.1017/nws.2014.4
Appears in Collections:Applied Mathematics and Mathematical Physics