Hopping in the Crowd to Unveil Network Topology

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

doi:10.1103/PhysRevLett.120.158301

Hopping in the Crowd to Unveil Network Topology

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

Research output: Contribution to journal › Letter

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.

Language	English
Article number	158301
Number of pages	5
Journal	Physical review letters
Volume	120
Issue number	15
DOIs	10.1103/PhysRevLett.120.158301
Publication status	Published - 9 Apr 2018

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topology

operators

estimates

Keywords

random walk
complex network
crowding
network reconstruction
non linear diffusion

Cite this

Asllani, M., Carletti, T., Di Patti, F., Fanelli, D., & Piazza, F. (2018). Hopping in the Crowd to Unveil Network Topology. Physical review letters, 120(15), [158301]. https://doi.org/10.1103/PhysRevLett.120.158301

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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title = "Hopping in the Crowd to Unveil Network Topology",

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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author = "Malbor Asllani and Timoteo Carletti and {Di Patti}, Francesca and Duccio Fanelli and Francesco Piazza",

year = "2018",

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doi = "10.1103/PhysRevLett.120.158301",

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Asllani, M , Carletti, T, Di Patti, F, Fanelli, D & Piazza, F 2018, 'Hopping in the Crowd to Unveil Network Topology' Physical review letters, vol. 120, no. 15, 158301. https://doi.org/10.1103/PhysRevLett.120.158301

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 journal › Letter

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

U2 - 10.1103/PhysRevLett.120.158301

DO - 10.1103/PhysRevLett.120.158301

M3 - Letter

VL - 120

JO - Physical review letters

T2 - Physical review letters

JF - Physical review letters