Diffusion capacity of single and interconnected networks

Abstract

Understanding diffusive processes in networks is a significant challenge in complexity science. Networks possess a diffusive potential that depends on their topological configuration, but diffusion also relies on the process and initial conditions. This article presents Diffusion Capacity, a concept that measures a node’s potential to diffuse information based on a distance distribution that considers both geodesic and weighted shortest paths and dynamical features of the diffusion process. Diffusion Capacity thoroughly describes the role of individual nodes during a diffusion process and can identify structural modifications that may improve diffusion mechanisms. The article defines Diffusion Capacity for interconnected networks and introduces Relative Gain, which compares the performance of a node in a single structure versus an interconnected one. The method applies to a global climate network constructed from surface air temperature data, revealing a significant change in diffusion capacity around the year 2000, suggesting a loss of the planet’s diffusion capacity that could contribute to the emergence of more frequent climatic events.Research partially supported by Brazilian agencies FAPEMIG, CAPES, and CNPq. P.M.P. acknowledges support from the “Paul and Heidi Brown Preeminent Professorship in ISE, University of Florida”, and RSF 14-41- 00039, Humboldt Research Award (Germany) and LATNA, Higher School of Economics, RF. C.M. acknowledges partial support from Spanish MINECO (PID2021-123994NB-C21) and ICREA ACADEMIA. A.D.- G. knowledges support from the Spanish grants PGC2018-094754-BC22 and PID2021-128005NB-C22, funded by MCIN/AEI/ 10.13039/ 501100011033 and “ERDF A way of making Europe”; and from Generalitat de Catalunya (2021SGR00856). M.G.R acknowledges partial support from FUNDEP.Peer ReviewedPostprint (published version

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