Hopping in the Crowd to Unveil Network Topology

Malbor Asllani, Timoteo Carletti, Francesca Di Patti, Duccio Fanelli, Francesco Piazza

Research output: Contribution to journalLetter

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.
LanguageEnglish
Article number158301
Number of pages5
JournalPhysical review letters
Volume120
Issue number15
DOIs
Publication statusPublished - 9 Apr 2018

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topology
operators
estimates

Keywords

  • random walk
  • complex network
  • crowding
  • network reconstruction
  • non linear diffusion

Cite this

Asllani, Malbor ; Carletti, Timoteo ; Di Patti, Francesca ; Fanelli, Duccio ; Piazza, Francesco. / Hopping in the Crowd to Unveil Network Topology. In: Physical review letters. 2018 ; Vol. 120, No. 15.
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Hopping in the Crowd to Unveil Network Topology. / Asllani, Malbor; Carletti, Timoteo; Di Patti, Francesca ; Fanelli, Duccio; Piazza, Francesco.

In: Physical review letters, Vol. 120, No. 15, 158301, 09.04.2018.

Research output: Contribution to journalLetter

TY - JOUR

T1 - Hopping in the Crowd to Unveil Network Topology

AU - Asllani, Malbor

AU - Carletti, Timoteo

AU - Di Patti, Francesca

AU - Fanelli, Duccio

AU - Piazza, Francesco

PY - 2018/4/9

Y1 - 2018/4/9

N2 - 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.

AB - 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.

KW - random walk

KW - complex network

KW - crowding

KW - network reconstruction

KW - non linear diffusion

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DO - 10.1103/PhysRevLett.120.158301

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