21,296 research outputs found
Information transfer in community structured multiplex networks
The study of complex networks that account for different types of
interactions has become a subject of interest in the last few years, specially
because its representational power in the description of users interactions in
diverse online social platforms (Facebook, Twitter, Instagram, etc.). The
mathematical description of these interacting networks has been coined under
the name of multilayer networks, where each layer accounts for a type of
interaction. It has been shown that diffusive processes on top of these
networks present a phenomenology that cannot be explained by the naive
superposition of single layer diffusive phenomena but require the whole
structure of interconnected layers. Nevertheless, the description of diffusive
phenomena on multilayer networks has obviated the fact that social networks
have strong mesoscopic structure represented by different communities of
individuals driven by common interests, or any other social aspect. In this
work, we study the transfer of information in multilayer networks with
community structure. The final goal is to understand and quantify, if the
existence of well-defined community structure at the level of individual
layers, together with the multilayer structure of the whole network, enhances
or deteriorates the diffusion of packets of information.Comment: 13 pages, 6 figure
Directionality reduces the impact of epidemics in multilayer networks
The study of how diseases spread has greatly benefited from advances in
network modeling. Recently, a class of networks known as multilayer graphs has
been shown to describe more accurately many real systems, making it possible to
address more complex scenarios in epidemiology such as the interaction between
different pathogens or multiple strains of the same disease. In this work, we
study in depth a class of networks that have gone unnoticed up to now, despite
of its relevance for spreading dynamics. Specifically, we focus on directed
multilayer networks, characterized by the existence of directed links, either
within the layers or across layers. Using the generating function approach and
numerical simulations of a stochastic susceptible-infected-susceptible (SIS)
model, we calculate the epidemic threshold for these networks for different
degree distributions of the networks. Our results show that the main feature
that determines the value of the epidemic threshold is the directionality of
the links connecting different layers, regardless of the degree distribution
chosen. Our findings are of utmost interest given the ubiquitous presence of
directed multilayer networks and the widespread use of disease-like spreading
processes in a broad range of phenomena such as diffusion processes in social
and transportation systems.Comment: 20 pages including 7 figures. Submitted for publicatio
Unique superdiffusion induced by directionality in multiplex networks
The multilayer network framework has served to describe and uncover a number of novel and unforeseen physical behaviors and regimes in interacting complex systems. However, the majority of existing studies are built on undirected multilayer networks while most complex systems in nature exhibit directed interactions. Here, we propose a framework to analyze diffusive dynamics on multilayer networks consisting of at least one directed layer. We rigorously demonstrate that directionality in multilayer networks can fundamentally change the behavior of diffusive dynamics: from monotonic (in undirected systems) to non-monotonic diffusion with respect to the interlayer coupling strength. Moreover, for certain multilayer network configurations, the directionality can induce a unique superdiffusion regime for intermediate values of the interlayer coupling, wherein the diffusion is even faster than that corresponding to the theoretical limit for undirected systems, i.e. the diffusion in the integrated network obtained from the aggregation of each layer. We theoretically and numerically show that the existence of superdiffusion is fully determined by the directionality of each layer and the topological overlap between layers. We further provide a formulation of multilayer networks displaying superdiffusion. Our results highlight the significance of incorporating the interacting directionality in multilevel networked systems and provide a framework to analyze dynamical processes on interconnected complex systems with directionality
Structural transition in interdependent networks with regular interconnections
Networks are often made up of several layers that exhibit diverse degrees of
interdependencies. A multilayer interdependent network consists of a set of
graphs that are interconnected through a weighted interconnection matrix , where the weight of each inter-graph link is a non-negative real number . Various dynamical processes, such as synchronization, cascading failures
in power grids, and diffusion processes, are described by the Laplacian matrix
characterizing the whole system. For the case in which the multilayer
graph is a multiplex, where the number of nodes in each layer is the same and
the interconnection matrix , being the identity matrix, it has
been shown that there exists a structural transition at some critical coupling,
. This transition is such that dynamical processes are separated into
two regimes: if , the network acts as a whole; whereas when , the network operates as if the graphs encoding the layers were isolated. In
this paper, we extend and generalize the structural transition threshold to a regular interconnection matrix (constant row and column sum).
Specifically, we provide upper and lower bounds for the transition threshold in interdependent networks with a regular interconnection matrix
and derive the exact transition threshold for special scenarios using the
formalism of quotient graphs. Additionally, we discuss the physical meaning of
the transition threshold in terms of the minimum cut and show, through
a counter-example, that the structural transition does not always exist. Our
results are one step forward on the characterization of more realistic
multilayer networks and might be relevant for systems that deviate from the
topological constrains imposed by multiplex networks.Comment: 13 pages, APS format. Submitted for publicatio
The physics of spreading processes in multilayer networks
The study of networks plays a crucial role in investigating the structure,
dynamics, and function of a wide variety of complex systems in myriad
disciplines. Despite the success of traditional network analysis, standard
networks provide a limited representation of complex systems, which often
include different types of relationships (i.e., "multiplexity") among their
constituent components and/or multiple interacting subsystems. Such structural
complexity has a significant effect on both dynamics and function. Throwing
away or aggregating available structural information can generate misleading
results and be a major obstacle towards attempts to understand complex systems.
The recent "multilayer" approach for modeling networked systems explicitly
allows the incorporation of multiplexity and other features of realistic
systems. On one hand, it allows one to couple different structural
relationships by encoding them in a convenient mathematical object. On the
other hand, it also allows one to couple different dynamical processes on top
of such interconnected structures. The resulting framework plays a crucial role
in helping achieve a thorough, accurate understanding of complex systems. The
study of multilayer networks has also revealed new physical phenomena that
remain hidden when using ordinary graphs, the traditional network
representation. Here we survey progress towards attaining a deeper
understanding of spreading processes on multilayer networks, and we highlight
some of the physical phenomena related to spreading processes that emerge from
multilayer structure.Comment: 25 pages, 4 figure
Spreading processes in Multilayer Networks
Several systems can be modeled as sets of interconnected networks or networks
with multiple types of connections, here generally called multilayer networks.
Spreading processes such as information propagation among users of an online
social networks, or the diffusion of pathogens among individuals through their
contact network, are fundamental phenomena occurring in these networks.
However, while information diffusion in single networks has received
considerable attention from various disciplines for over a decade, spreading
processes in multilayer networks is still a young research area presenting many
challenging research issues. In this paper we review the main models, results
and applications of multilayer spreading processes and discuss some promising
research directions.Comment: 21 pages, 3 figures, 4 table
Multilayer Networks in a Nutshell
Complex systems are characterized by many interacting units that give rise to
emergent behavior. A particularly advantageous way to study these systems is
through the analysis of the networks that encode the interactions among the
system's constituents. During the last two decades, network science has
provided many insights in natural, social, biological and technological
systems. However, real systems are more often than not interconnected, with
many interdependencies that are not properly captured by single layer networks.
To account for this source of complexity, a more general framework, in which
different networks evolve or interact with each other, is needed. These are
known as multilayer networks. Here we provide an overview of the basic
methodology used to describe multilayer systems as well as of some
representative dynamical processes that take place on top of them. We round off
the review with a summary of several applications in diverse fields of science.Comment: 16 pages and 3 figures. Submitted for publicatio
An ensemble perspective on multi-layer networks
We study properties of multi-layered, interconnected networks from an
ensemble perspective, i.e. we analyze ensembles of multi-layer networks that
share similar aggregate characteristics. Using a diffusive process that evolves
on a multi-layer network, we analyze how the speed of diffusion depends on the
aggregate characteristics of both intra- and inter-layer connectivity. Through
a block-matrix model representing the distinct layers, we construct transition
matrices of random walkers on multi-layer networks, and estimate expected
properties of multi-layer networks using a mean-field approach. In addition, we
quantify and explore conditions on the link topology that allow to estimate the
ensemble average by only considering aggregate statistics of the layers. Our
approach can be used when only partial information is available, like it is
usually the case for real-world multi-layer complex systems
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