Hopping in the Crowd to Unveil Network Topology

Physical Review Letters
Malbor AsllaniFrancesco Piazza

Abstract

We introduce a nonlinear operator to model diffusion on a complex undirected network under crowded conditions. We show that the asymptotic distribution of diffusing agents is a nonlinear function of the nodes' degree and saturates to a constant value for sufficiently large connectivities, at variance with standard diffusion in the absence of excluded-volume effects. Building on this observation, we define and solve an inverse problem, aimed at reconstructing the a priori unknown connectivity distribution. The method gathers all the necessary information by repeating a limited number of independent measurements of the asymptotic density at a single node, which can be chosen randomly. The technique is successfully tested against both synthetic and real data and is also shown to estimate with great accuracy the total number of nodes.

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Citations

Nov 6, 2018·Scientific Reports·Giulia CencettiDuccio Fanelli
Mar 15, 2020·Physical Review. E·Timoteo CarlettiDuccio Fanelli
Mar 20, 2021·Physical Review. E·Gloria CecchiniArkady Pikovsky

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