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Loop-centrality in complex networks

P. Giscard,Richard C. Wilson

Published 2017 in International Workshop on Complex Networks & Their Applications

ABSTRACT

Cycles (loops) on networks represent feedback processes which play a central role in dynamical self-regulation and resiliency against perturbations in complex systems. In spite of a flurry of research from biology to economy into such phenomenon, there is no established measure of importance for individual loops. We introduce a centrality measure to this effect, which quantifies the fraction of the total information flow of the network passing through a loop. This measure is computationally cheap, numerically well-conditioned, induces a centrality measure on arbitrary subgraphs and reduces to the eigenvector centrality on vertices. As an illustration, we study the centrality of strategic ensembles of sectors in the input-output macro-economic model of four countries over the 2000-2014 period. We find the results to accurately reflect the structures of these countries' economies. In particular, the evolution of the centrality of the finance-real estate-insurance clique in the US economy clearly shows the effects of deregulation, crashes, bail-outs, and even novel legislations. These insights are not replicated by vertex-centralities. Finally, we study the PPI of the plant Arabidopsis thaliana. We propose a model of plant-pathogen interactions where the latter primarily aim at maximising the fraction of disrupted sequences of protein reactions in their host. This translates into pathogen-targeted-proteins being concentrated in a small number of triads with high loop-centrality. We show that this model better accounts for the observations than the state-of-the-art one, built from a vertex-centrality.

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