  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.
