Hopping in the Crowd to Unveil Network Topology

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

Research output: Contribution to journalLetter

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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.
Original languageEnglish
Article number158301
Number of pages5
JournalPhysical review letters
Issue number15
Publication statusPublished - 9 Apr 2018


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

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  • Projects

    PAI n°P7/19 - DYSCO: Dynamical systems, control and optimization (DYSCO)

    WINKIN, J., Blondel, V., Vandewalle, J., Pintelon, R., Sepulchre, R., Vande Wouwer, A. & SARTENAER, A.


    Project: Research


    • 1 Participation in conference
    • 1 Invited talk

    Conference on Complex Systems 2018

    Timoteo Carletti (Contributor)

    24 Sep 201828 Sep 2018

    Activity: Participating in or organising an event typesParticipation in conference

    Hopping in the crowd to unveil network topology

    Timoteo Carletti (Speaker)

    24 Sep 2018

    Activity: Talk or presentation typesInvited talk

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