Abrupt transition in the structural formation of interconnected networks
Filippo Radicchi,Alex Arenas +1 more
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TLDR
In this paper, a model of an interdependent network of networks is presented, and it is shown that an abrupt phase transition occurs when interconnections between independent networks are added.Abstract:
Real-world networks are rarely isolated. A model of an interdependent network of networks shows that an abrupt phase transition occurs when interconnections between independent networks are added. This study also suggests ways to minimize the danger of abrupt structural changes to real networks.read more
Citations
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The structure and dynamics of multilayer networks
Stefano Boccaletti,Ginestra Bianconi,Regino Criado,Regino Criado,C.I. del Genio,Jesús Gómez-Gardeñes,Miguel Romance,Miguel Romance,Irene Sendiña-Nadal,Irene Sendiña-Nadal,Zhen Wang,Massimiliano Zanin +11 more
TL;DR: This work offers a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.
Journal ArticleDOI
Multilayer Networks
TL;DR: In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications.
Journal ArticleDOI
Mathematical Formulation of Multilayer Networks
Manlio De Domenico,Albert Solé-Ribalta,Emanuele Cozzo,Mikko Kivelä,Yamir Moreno,Mason A. Porter,Sergio Gómez,Alex Arenas +7 more
TL;DR: In this paper, a tensorial framework for multilayer complex networks is introduced, and several important network descriptors and dynamical processes such as degree centrality, clustering coefficients, eigenvector centrality and modularity are discussed.
Journal ArticleDOI
Mathematical Formulation of Multi-Layer Networks
Manlio De Domenico,Albert Solé-Ribalta,Emanuele Cozzo,Mikko Kivelä,Yamir Moreno,Mason A. Porter,Sergio Gómez,Alex Arenas +7 more
TL;DR: In this article, a tensorial framework for multi-layer networks is introduced, and several important network descriptors and dynamical processes such as degree centrality, clustering coefficients, eigenvector centrality and modularity, Von Neumann entropy, and diffusion are discussed.
Journal ArticleDOI
Human mobility: Models and applications
Hugo Barbosa,Marc Barthelemy,Gourab Ghoshal,Charlotte R James,Maxime Lenormand,Thomas Louail,Ronaldo Menezes,José J. Ramasco,Filippo Simini,Marcello Tomasini +9 more
TL;DR: This survey reviews the approaches developed to reproduce various mobility patterns, with the main focus on recent developments, and organizes the subject by differentiating between individual and population mobility and also between short-range and long-range mobility.
References
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TL;DR: Eigenvalues and the Laplacian of a graph Isoperimetric problems Diameters and eigenvalues Paths, flows, and routing Eigen values and quasi-randomness