6,334 research outputs found
Effects of temporal correlations in social multiplex networks
Multi-layered networks represent a major advance in the description of natural complex systems, and their study has shed light on new physical phenomena. Despite its importance, however, the role of the temporal dimension in their structure and function has not been investigated in much detail so far. Here we study the temporal correlations between layers exhibited by real social multiplex networks. At a basic level, the presence of such correlations implies a certain degree of predictability in the contact pattern, as we quantify by an extension of the entropy and mutual information analyses proposed for the single-layer case. At a different level, we demonstrate that temporal correlations are a signature of a ‘multitasking’ behavior of network agents, characterized by a higher level of switching between different social activities than expected in a uncorrelated pattern. Moreover, temporal correlations significantly affect the dynamics of coupled epidemic processes unfolding on the network. Our work opens the way for the systematic study of temporal multiplex networks and we anticipate it will be of interest to researchers in a broad array of fields
Multilayer Networks
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. Such
systems include multiple subsystems and layers of connectivity, and it is
important to take such "multilayer" features into account to try to improve our
understanding of complex systems. Consequently, it is necessary to generalize
"traditional" network theory by developing (and validating) a framework and
associated tools to study multilayer systems in a comprehensive fashion. The
origins of such efforts date back several decades and arose in multiple
disciplines, and now the study of multilayer networks has become one of the
most important directions in network science. In this paper, we discuss the
history of multilayer networks (and related concepts) and review the exploding
body of work on such networks. To unify the disparate terminology in the large
body of recent work, we discuss a general framework for multilayer networks,
construct a dictionary of terminology to relate the numerous existing concepts
to each other, and provide a thorough discussion that compares, contrasts, and
translates between related notions such as multilayer networks, multiplex
networks, interdependent networks, networks of networks, and many others. We
also survey and discuss existing data sets that can be represented as
multilayer networks. We review attempts to generalize single-layer-network
diagnostics to multilayer networks. We also discuss the rapidly expanding
research on multilayer-network models and notions like community structure,
connected components, tensor decompositions, and various types of dynamical
processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure
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
A framework for the construction of generative models for mesoscale structure in multilayer networks
Multilayer networks allow one to represent diverse and coupled connectivity patterns—such as time-dependence, multiple subsystems, or both—that arise in many applications and which are difficult or awkward to incorporate into standard network representations. In the study of multilayer networks, it is important to investigate mesoscale (i.e., intermediate-scale) structures, such as dense sets of nodes known as communities, to discover network features that are not apparent at the microscale or the macroscale. The ill-defined nature of mesoscale structure and its ubiquity in empirical networks make it crucial to develop generative models that can produce the features that one encounters in empirical networks. Key purposes of such models include generating synthetic networks with empirical properties of interest, benchmarking mesoscale-detection methods and algorithms, and inferring structure in empirical multilayer networks. In this paper, we introduce a framework for the construction of generative models for mesoscale structures in multilayer networks. Our framework provides a standardized set of generative models, together with an associated set of principles from which they are derived, for studies of mesoscale structures in multilayer networks. It unifies and generalizes many existing models for mesoscale structures in fully ordered (e.g., temporal) and unordered (e.g., multiplex) multilayer networks. One can also use it to construct generative models for mesoscale structures in partially ordered multilayer networks (e.g., networks that are both temporal and multiplex). Our framework has the ability to produce many features of empirical multilayer networks, and it explicitly incorporates a user-specified dependency structure between layers. We discuss the parameters and properties of our framework, and we illustrate examples of its use with benchmark models for community-detection methods and algorithms in multilayer networks
Mathematical Formulation of Multi-Layer Networks
A network representation is useful for describing the structure of a large
variety of complex systems. However, most real and engineered systems have
multiple subsystems and layers of connectivity, and the data produced by such
systems is very rich. Achieving a deep understanding of such systems
necessitates generalizing "traditional" network theory, and the newfound deluge
of data now makes it possible to test increasingly general frameworks for the
study of networks. In particular, although adjacency matrices are useful to
describe traditional single-layer networks, such a representation is
insufficient for the analysis and description of multiplex and time-dependent
networks. One must therefore develop a more general mathematical framework to
cope with the challenges posed by multi-layer complex systems. In this paper,
we introduce a tensorial framework to study multi-layer networks, and we
discuss the generalization of several important network descriptors and
dynamical processes --including degree centrality, clustering coefficients,
eigenvector centrality, modularity, Von Neumann entropy, and diffusion-- for
this framework. We examine the impact of different choices in constructing
these generalizations, and we illustrate how to obtain known results for the
special cases of single-layer and multiplex networks. Our tensorial approach
will be helpful for tackling pressing problems in multi-layer complex systems,
such as inferring who is influencing whom (and by which media) in multichannel
social networks and developing routing techniques for multimodal transportation
systems.Comment: 15 pages, 5 figure
Quantifying dynamical spillover in co-evolving multiplex networks
Multiplex networks (a system of multiple networks that have different types
of links but share a common set of nodes) arise naturally in a wide spectrum of
fields. Theoretical studies show that in such multiplex networks, correlated
edge dynamics between the layers can have a profound effect on dynamical
processes. However, how to extract the correlations from real-world systems is
an outstanding challenge. Here we provide a null model based on Markov chains
to quantify correlations in edge dynamics found in longitudinal data of
multiplex networks. We use this approach on two different data sets: the
network of trade and alliances between nation states, and the email and
co-commit networks between developers of open source software. We establish the
existence of "dynamical spillover" showing the correlated formation (or
deletion) of edges of different types as the system evolves. The details of the
dynamics over time provide insight into potential causal pathways
Analytical computation of the epidemic threshold on temporal networks
The time variation of contacts in a networked system may fundamentally alter
the properties of spreading processes and affect the condition for large-scale
propagation, as encoded in the epidemic threshold. Despite the great interest
in the problem for the physics, applied mathematics, computer science and
epidemiology communities, a full theoretical understanding is still missing and
currently limited to the cases where the time-scale separation holds between
spreading and network dynamics or to specific temporal network models. We
consider a Markov chain description of the Susceptible-Infectious-Susceptible
process on an arbitrary temporal network. By adopting a multilayer perspective,
we develop a general analytical derivation of the epidemic threshold in terms
of the spectral radius of a matrix that encodes both network structure and
disease dynamics. The accuracy of the approach is confirmed on a set of
temporal models and empirical networks and against numerical results. In
addition, we explore how the threshold changes when varying the overall time of
observation of the temporal network, so as to provide insights on the optimal
time window for data collection of empirical temporal networked systems. Our
framework is both of fundamental and practical interest, as it offers novel
understanding of the interplay between temporal networks and spreading
dynamics.Comment: 22 pages, 6 figure
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