### Abstract

Language | English |
---|---|

Article number | 158301 |

Number of pages | 5 |

Journal | Physical Review Letters |

Volume | 120 |

Issue number | 15 |

DOIs | |

State | Published - 9 Apr 2018 |

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### Keywords

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

### Cite this

*Physical Review Letters*,

*120*(15), [158301]. DOI: 10.1103/PhysRevLett.120.158301

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*Physical Review Letters*, vol. 120, no. 15, 158301. DOI: 10.1103/PhysRevLett.120.158301

**Hopping in the Crowd to Unveil Network Topology.** / Asllani, Malbor; Carletti, Timoteo; Di Patti, Francesca ; Fanelli, Duccio; Piazza, Francesco.

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

SN - 0031-9007

IS - 15

M1 - 158301

ER -