Network Theory

Multiplex Networks

“Disease Localization in Multilayer Networks “

**Physical Review X**

**7**, 011014 (2017)

G. Ferraz de Arruda, E. Cozzo, T. P. Peixoto, F. A. Rodrigues, and Y. Moreno

Abstract

We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the susceptible-infected-susceptible (SIS) and susceptible-infected-recovered dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasistationary state method, we numerically show the existence of disease localization and the emergence of two or more susceptibility peaks, which are characterized analytically and numerically through the inverse participation ratio. At variance with what is observed in single-layer networks, we show that disease localization takes place on the layers and not on the nodes of a given layer. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe a characteristic transition in the eigenvalue spectra of the supra-contact tensor as a function of the ratio of two spreading rates: If the rate at which the disease spreads within a layer is comparable to the spreading rate across layers, the individual spectra of each layer merge with the coupling between layers. Finally, we report on an interesting phenomenon, the barrier effect; i.e., for a three-layer configuration, when the layer with the lowest eigenvalue is located at the center of the line, it can effectively act as a barrier to the disease. The formalism introduced here provides a unifying mathematical approach to disease contagion in multiplex systems, opening new possibilities for the study of spreading processes.

“Characterization of multiple topological scales in multiplex networks through supra-Laplacian eigengaps”

**Physical Review E**

**94**, 052318 (2016)

E. Cozzo and Y. Moreno

“Lévy random walks on multiplex networks”

**Scientific Reports**

**6**, 37641 (2016)

Q. Guo, E. Cozzo, Z. Zheng, and Y. Moreno

“On degree-degree correlations in multilayer networks”

**Physica D**

**323-324**, 5 (2016)

G. Ferraz de Arruda, E. Cozzo, Y. Moreno, and F. A. Rodrigues

“Multilayer networks: metrics and spectral properties”

**Chapter contribution**to the book

**“Interconnected networks”**, edited by F. Schweitzer and A. Garas. ISBN 978-3-319-23947-7, Springer (2016).

E. Cozzo, G. Ferraz de Arruda, F. A. Rodrigues, and Y. Moreno

“Dimensionality reduction and spectral properties of multilayer networks”

**Physical Review E**

**89**, 052815 (2014)

R. Sánchez-Garcia, E. Cozzo, and Y. Moreno

“Structure of Triadic Relations in Multiplex Networks”

**New Journal of Physics**

**17**, 073029 (2015)

E. Cozzo, M. Kivela, M. De Domenico, A. Sole-Ribalta, A. Arenas, S. Gómez, M. A. Porter, and Y. Moreno

“Dynamics of interacting diseases”

**Physical Review X**

**4**, 041005 (2014)

J. Sanz, C.-Y. Xia, S. Meloni and Y. Moreno

Abstract

Current modeling of infectious diseases allows for the study of complex and realistic scenarios that go from the population to the individual level of description. However, most epidemic models assume that the spreading process takes place on a single level (be it a single population, a metapopulation system, or a network of contacts). In particular, interdependent contagion phenomena can be addressed only if we go beyond the scheme-one pathogen-one network. In this paper, we propose a framework that allows us to describe the spreading dynamics of two concurrent diseases. Specifically, we characterize analytically the epidemic thresholds of the two diseases for different scenarios and compute the temporal evolution characterizing the unfolding dynamics. Results show that there are regions of the parameter space in which the onset of a disease’s outbreak is conditioned to the prevalence levels of the other disease. Moreover, we show, for the susceptible-infected-susceptible scheme, that under certain circumstances, finite and not vanishing epidemic thresholds are found even at the limit for scale-free networks. For the susceptible- infected-removed scenario, the phenomenology is richer and additional interdependencies show up. We also find that the secondary thresholds for the susceptible-infected-susceptible and susceptible- infected-removed models are different, which results directly from the interaction between both diseases. Our work thus solves an important problem and paves the way toward a more comprehensive description of the dynamics of interacting diseases.

“Multilayer Networks”

**Journal of Complex Networks**

**2**, 203-271 (2014)

M. Kivela, A. Arenas, M. Barthelemy, J. P. Gleeson, Y. Moreno, and M. A. Porter

“Contact-based social contagion in multiplex networks”

**Physical Review E (RC)**

**88**, 050801 (2013)

E. Cozzo, R. A. Baños, S. Meloni, and Y. Moreno

“Mathematical formulation of multi-layer networks”

**Physical Review X**

**3**, 041022 (2013)

M. De Domenico, A. Sole-Ribalta, E. Cozzo, M. Kivela, Y. Moreno, M. A. Porter, S. Gómez, and A. Arenas

“Stability of Boolean Multilevel Networks”

**Physical Review E**

**86**, 036115 (2012)

E. Cozzo, A. Arenas, and Y. Moreno

Synchronization

“Generalized synchronization in relay systems”

**Physical Review E**

**88**, 052908 (2013)

R. Gutiérrez, R. Sevilla-Escoboza, P. Piedrahita, C. Finke, U. Feudel, J. M. Buldú, G. Huerta-Cuellar, R. Jaimes-Reátegui, Y. Moreno, and S. Boccaletti

“Non-equilibrium first-order transition to synchrony in networks of chaotic oscillators”

**Physical Review Letters**

**108**, 168702 (2012)

I. Leyva, R. Sevilla-Escoboza, J. M. Buldu, I. Sendiña-Nadal, J. Gómez-Gardeñes, A. Arenas, Y. Moreno, S. Gómez, R. Jaimes-Reátegui, and S. Boccaletti

“Evolution of Microscopic and Mesoscopic Synchronized Patterns in Complex Networks”

**Chaos**

**21**, 016105 (2011)

J. Gomez-Gardeñes, Y. Moreno, and A. Arenas

“Explosive Synchronization Transitions in Scale-Free Networks”

**Physical Review Letters**

**106**, 128701 (2011)

J. Gomez-Gardeñes, Y. Moreno, and A. Arenas

“Synchronization of Kuramoto oscillators in Random Geometric Graphs”

**International Journal of Bifurcation and Chaos**

**19**, 687-693 (2009)

A. Díaz-Guilera, J. Gomez-Gardeñes, Y. Moreno, M. Nekovee

“Synchronization in Complex Networks”

**Physics Reports**

**469**, 93-153 (2008). (Report on Synchronization)

A. Arenas, A. Diaz-Guilera,J.Kurths, Y. Moreno,and C. Zhou

Abstract

Synchronization processes in populations of locally interacting elements are the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understanding synchronization phenomena in natural systems now take advantage of the recent theory of complex networks.In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also take an overview of the new emergent features coming out from the interplay between the structure and the function of the underlying patterns of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.

“Synchronization of networks with variable local properties”

**International Journal of Bifurcation and Chaos**

**17**, 92501 (2007)

J. Gomez-Gardeñes, and Y. Moreno

“Paths to Synchronization on Complex Networks”

**Physical Review Letters**

**98**, 034101 (2007)

J. Gomez-Gardeñes, Y. Moreno, and A. Arenas

“Fitness for Synchronization of Network Motifs”

**Physica A**

**343**, 034101 (2007)

Y. Moreno, M. Vazquez-Prada, and A. F. Pacheco

“Synchronization of Kuramoto Oscillators in Scale-Free Networks”

**Europhysics Letters**

**68**, 603 (2004)

Y. Moreno, and A. F. Pacheco

Network Structure

“The role of centrality for the identification of influential spreaders in complex networks”

**Submitted for publication**

G. Ferraz de Arruda, A. Luiz Barbieri, P. Martin Rodríguez, Y. Moreno, L. da Fontoura Costa, and F. A. Rodrígues

“Scaling breakdown in flow fluctuations on complex networks”

**Physical Review Letters**

**100**, 208701 (2008)

S. Meloni, J. Gomez-Gardeñes, V. Latora and Y. Moreno

“Focus on Complex Networked Systems: Theory and Application”

**New Journal of Physics**

**100**, (2007) (Editorial to the Focus Issue)

S. Havlin, M. Nekovee, and Y. Moreno

“Complex Networks: Structure and Dynamics”

**Physics Reports**

**424**, 175-308 (2006)

S. Boccaletti, V. Latora, Y. Moreno, M. Chavez and D.-U. Hwang

Abstract

Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highly interconnected dynamical units. The first approach to capture the global properties of such systems is to model them as graphs whose nodes represent the dynamical units, and whose links stand for the interactions between them. On the one hand, scientists have to cope with structural issues, such as characterizing the topology of a complex wiring architecture, revealing the unifying principles that are at the basis of real networks, and developing models to mimic the growth of a network and reproduce its structural properties. On the other hand, many relevant questions arise when studying complex networks’ dynamics, such as learning how a large ensemble of dynamical systems that interact through a complex wiring topology can behave collectively. We review the major concepts and results recently achieved in the study of the structure and dynamics of complex networks, and summarize the relevant applications of these ideas in many different disciplines, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.

“From Scale-Free to Erdos-Renyi Networks”

**Physical Review E**

**73**, 056124 (2006)

J. Gomez-Gardeñes and Y. Moreno

“Scale-Free topologies and Activatory-Inhibitory interactions”

**Chaos**(Focus Issue)

**16**, 015114 (2006)

J. Gomez-Gardeñes, Y. Moreno, and L. M. Floria

“Structure of peer-to-peer social networks”

**Physical Review E**

**73**, 036123 (2006)

F. Wang, Y. Moreno, and Y. Sun

“Distance-d covering problems in scale-free networks with degree correlations”

**Physical Review E**

**71**, 035102(R) (2005)

P. Echenique, J. Gomez-Gardeñes, Y. Moreno, and A. Vazquez

“Dynamics of Rumor Spreading in Complex Networks”

**Physical Review E**

**69**, 066130 (2004)

Y. Moreno, M. Nekovee, A. F. Pacheco

“Efficiency and Reliability of Epidemic Data Dissemination in Complex Networks”

**Physical Review E**

**69**, 055101(R) (2004)

Y. Moreno, M. Nekovee, A. Vespignani

“Local versus Global Knowledge in the Barabasi-Albert Scale-free Network Model”

**Physical Review E**

**69**, 037103 (2004)

J. Gomez-Gardeñes, and Y. Moreno

“Topology and Correlations in Structured Scale-Free Networks”

**Physical Review E**

**67**, 046111 (2003)

A. Vazquez, M. Boguñá, Y. Moreno, R. Pastor-Satorras, A. Vespignani

Critical Phenomena

“Critical Load and Traffic Instabilities in Scale-Free Networks”

**Europhysics Letters**

**62**, 046111 (2003)

Y. Moreno, R. Pastor-Satorras, A. Vazquez, A. Vespignani

“Resilience to Damage of Graphs with Degree Correlations”

**Physical Review E**

**67**, 015101(R) (2003)

A. Vazquez, Y. Moreno

“Error Diagrams and Temporal Correlations in a Fracture Model with Characteristic and Power-Law Distributed Avalanches”

**European Physical Journal B**

**34**, 489 (2003)

Y. Moreno, M. Vazquez-Prada, J. B. Gomez, A. F. Pacheco

“Creep Rupture has two Universality Classes”

**Europhysics Letters**

**67**, 347 (2003)

F. Kun, Y. Moreno, R. Cruz, H. J. Herrmann

“Inestability of scale-free networks under node-breaking avalanches”

**Europhysics Letters**

**58**, 630 (2002)

Y. Moreno, J. B. Gomez, A. F. Pacheco

“The Bak-Sneppen Model on Scale-Free Networks”

**Europhysics Letters**

**57**, 765 (2002)

Y. Moreno, A. Vazquez

“Fracture and Second-Order Phase Transitions”

**Physical Review Letters**

**85**, 2865 (2000)

Y. Moreno, J. B. Gomez, A. F. Pacheco

“Probabilistic Approach to Time-Dependent Load-Transfer Models of Fracture”

**Physical Review E**

**58**, 1528 (1998)

J. B. Gomez, Y. Moreno, A. F. Pacheco