Universality of eigenvector delocalization and the nature of the SIS phase transition in multiplex networks

Published on May 16, 2020in arXiv: Physics and Society
Guilherme Ferraz de Arruda5
Estimated H-index: 5
J. A. Méndez-Bermúdez9
Estimated H-index: 9
+ 1 AuthorsYamir Moreno55
Estimated H-index: 55
Universal spectral properties of multiplex networks allow us to assess the nature of the transition between disease-free and endemic phases in the SIS epidemic spreading model. In a multiplex network, depending on a coupling parameter, p the inverse participation ratio (IPR of the leading eigenvector of the adjacency matrix can be in two different structural regimes: (i) layer-localized and (ii) delocalized. Here we formalize the structural transition point, p^* between these two regimes, showing that there are universal properties regarding both the layer size nand the layer configurations. Namely, we show that IPR \sim n^{-\delta} with \delta\approx 1 and revealed an approximately linear relationship between p^*and the difference between the layers' average degrees. Furthermore, we showed that this multiplex structural transition is intrinsically connected with the nature of the SIS phase transition, allowing us to both understand and quantify the phenomenon. As these results are related to the universal properties of the leading eigenvector, we expect that our findings might be relevant to other dynamical processes in complex networks.
  • References (6)
  • Citations (0)
📖 Papers frequently viewed together
8 Citations
3 Authors (Rajesh Kumar, ..., Hocine Cherifi)
78% of Scinapse members use related papers. After signing in, all features are FREE.
#1Ginestra Bianconi (QMUL: Queen Mary University of London)H-Index: 39
Multilayer networks are emerging as a novel and powerful way to describe complex systems. Multilayer networks are ubiquitous and include social networks, financial markets, infrastructures, molecular networks and the brain. Uncovering the interplay between multilayer network structure and function is a big theoretical challenge with a vast realm of applications. On the other side the urgency of understanding real-world multilayer network problems requires novel theoretical approaches. In this ta...
31 Citations
#1Piet Van Mieghem (TU Delft: Delft University of Technology)H-Index: 47
Analyzing the behavior of complex networks is an important element in the design of new man-made structures such as communication systems and biologically engineered molecules. Because any complex network can be represented by a graph, and therefore in turn by a matrix, graph theory has become a powerful tool in the investigation of network performance. This self-contained book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks. C...
365 Citations
#1Mark NewmanH-Index: 89
The scientific study of networks, including computer networks, social networks, and biological networks, has received an enormous amount of interest in the last few years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on a large scale, and the development of a variety of new theoretical tools has allowed us to extract new knowledge from many different kinds of networks.The study of networks is broadly interdis...
5,855 Citations
#1Alain BarratH-Index: 46
#2Marc BarthlemyH-Index: 1
Last. Alessandro VespignaniH-Index: 88
view all 3 authors...
The availability of large data sets have allowed researchers to uncover complex properties such as large scale fluctuations and heterogeneities in many networks which have lead to the breakdown of standard theoretical frameworks and models. Until recently these systems were considered as haphazard sets of points and connections. Recent advances have generated a vigorous research effort in understanding the effect of complex connectivity patterns on dynamical phenomena. For example, a vast number...
1,221 Citations
#1Joaquín MarroH-Index: 20
#2Ronald DickmanH-Index: 33
Preface 1. Introduction 2. Driven lattice gases: simulations 3. Driven lattice gases: theory 4. Lattice gases with reaction 5. Catalysis models 6. The contact process 7. Models of disorder 8. Conflicting dynamics 9. Particle reaction models Bibliography Index.
886 Citations
#1H. Eugene StanleyH-Index: 118
#2Guenter AhlersH-Index: 47
This is a paperback edition of a distinguished book, originally published by Clarendon Press in 1971. It was then the first text on critical phenomena, a field that has enjoyed great activity for the past twenty years and that still continues to attract much attention. The book is at the level at which a graduate student who has studied condensed matter physics can begin to comprehend the nature of phase transitions, which involve the transformation of one state of matter into another. (A simple...
3,582 Citations
Cited By0