On metrics and models for multiplex networks

Gemmetto, V. (2018)

Doctoral Thesis

In this thesis, we extend the concept of null models as canonical ensembles of multi-graphs with given constraints and present new metrics able to characterize real-world layered systems based on their correlation patterns. We make extensive use of the maximum-entropy method in order to find the analytical expression of the expectation values of several topological quantities; furthermore, we employ the maximum-likelihood method to fit the models to real datasets. One of the main contributions of the present work is providing models and metrics that can be directly applied to real data. We introduce improved measures of overlap between layers of a multiplex and exploit such quantities to provide a new network reconstruction method applicable to multi-layer graphs. It turns out that this methodology, applicable to a specific class of multi-layer networks, can be successfully employed to reconstruct the World Trade Multiplex. Furthermore, we illustrate that the maximum-entropy models also allow us to find the so-called backbone of a real network, i.e. the information which is irreducible to the single-node properties and is therefore peculiar to the network itself. We conclude the thesis moving our attention to a different dataset, namely the scientific publication system.

• Complex systems
• Complex networks
• Multiplex networks
• Graph theory
• International trade
• Scientific publications network

• All authors: Gemmetto, V.
• Supervisor: Saarloos, W. van
• Co-supervisor: Garlaschelli, D.
• Committee: Caldarelli, G.; Serrano, M.A.; Eliel, E.R.; Hollander, W.T.F. den; Ruitenbeek, J.M. van; Emmerich, M.
• Qualification: Doctor (dr.)
• Awarding Institution: Lorentz Institute for Theoretical Physics, Science, Leiden University
• Date: 2018-01-16
• ISBN (print): 9789085933298