11–13 Dec 2019
Salone degli Affreschi, Palazzo Ateneo Università "Aldo Moro" Bari
Europe/Rome timezone
SM&FT 2019 Challenges in Computational Theoretical Physics

Grand canonical ensemble of heterogeneous weighted networks

11 Dec 2019, 14:45
30m
Salone degli Affreschi, Palazzo Ateneo Università "Aldo Moro" Bari

Salone degli Affreschi, Palazzo Ateneo Università "Aldo Moro" Bari

Piazza Umberto I, 1 Bari

Speaker

Andrea Gabrielli (Dipartimento di Ingegneria, Università degli Studi Roma Tre)

Description

In the last years the formulation of statistical ensembles of binary and weighted random graphs satisfying some arbitrary constraints has attracted much attention in phys/math communities for its two-fold potential application [1, 2]: (i) The construction of appropriate null models for the statistical validation of high order properties of real networks; (ii) the reconstruction of the statistical properties of real network starting for partial accessible information. The cornerstone of the statistical physics of complex networks is the idea that the links, and not the nodes, are the effective particles of the system. Here we formulate a mapping between weighted networks and lattice gasses, making the conceptual step forward of interpreting weighted links as particles with a generalised coordinate [3]. This leads to the definition of the grand canonical ensemble of weighted complex networks. We derive exact expressions for the partition function and thermodynamic quantities, both in the cases of global and local (i.e., node-specific) constraints on density and mean energy of particles. We further show that, when modeling real cases of networks, the binary and weighted statistics of the ensemble can be disentangled, leading to a simplified framework for a range of practical applications.

References
[1] T. Squartini, G. Caldarelli, G. Cimini, A. Gabrielli, D, Garlaschelli, Phys. Reports 757, 1-47 (2018).
[2] G. Cimini, T. Squartini, F. Saracco, D. Garlaschelli, A. Gabrielli, G. Caldarelli, Nature Review Physics 1, 58-71 (2019).
[3] A. Gabrielli, R. Mastrandrea, G. Caldarelli, G. Cimini, Phys. Rev. E 99, 030301(R) (2019)

Primary author

Andrea Gabrielli (Dipartimento di Ingegneria, Università degli Studi Roma Tre)

Co-authors

Prof. Guido Caldarelli (IMT - Lucca) Dr Giulio Cimini (Dipartimento di Fisica, Università "Tor Vergata" di Roma) Dr Rossana Mastrandrea (IMT - Lucca)

Presentation materials