2 research outputs found
Cycle-centrality in complex networks
Networks are versatile representations of the interactions between entities
in complex systems. Cycles on such networks represent feedback processes which
play a central role in system dynamics. In this work, we introduce a measure of
the importance of any individual cycle, as the fraction of the total
information flow of the network passing through the cycle. This measure is
computationally cheap, numerically well-conditioned, induces a centrality
measure on arbitrary subgraphs and reduces to the eigenvector centrality on
vertices. We demonstrate that this measure accurately reflects the impact of
events on strategic ensembles of economic sectors, notably in the US economy.
As a second example, we show that in the protein-interaction network of the
plant Arabidopsis thaliana, a model based on cycle-centrality better accounts
for pathogen activity than the state-of-art one. This translates into
pathogen-targeted-proteins being concentrated in a small number of triads with
high cycle-centrality. Algorithms for computing the centrality of cycles and
subgraphs are available for download
A centrality measure for cycles and subgraphs II
In a recent work we introduced a measure of importance for groups of vertices in a complex network. This centrality for groups is always between 0 and 1 and induces the eigenvector centrality over vertices. Furthermore, its value over any group is the fraction of all network flows intercepted by this group. Here we provide the rigorous mathematical constructions underpinning these results via a semi-commutative extension of a number theoretic sieve. We then established further relations between the eigenvector centrality and the centrality proposed here, showing that the latter is a proper extension of the former to groups of nodes. We finish by comparing the centrality proposed here with the notion of group-centrality introduced by Everett and Borgatti on two real-world networks: the Wolfe’s dataset and the protein-protein interaction network of the yeast Saccharomyces cerevisiae. In this latter case, we demonstrate that the centrality is able to distinguish protein complexe