89,017 research outputs found
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
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
Community detection in temporal multilayer networks, with an application to correlation networks
Networks are a convenient way to represent complex systems of interacting
entities. Many networks contain "communities" of nodes that are more densely
connected to each other than to nodes in the rest of the network. In this
paper, we investigate the detection of communities in temporal networks
represented as multilayer networks. As a focal example, we study time-dependent
financial-asset correlation networks. We first argue that the use of the
"modularity" quality function---which is defined by comparing edge weights in
an observed network to expected edge weights in a "null network"---is
application-dependent. We differentiate between "null networks" and "null
models" in our discussion of modularity maximization, and we highlight that the
same null network can correspond to different null models. We then investigate
a multilayer modularity-maximization problem to identify communities in
temporal networks. Our multilayer analysis only depends on the form of the
maximization problem and not on the specific quality function that one chooses.
We introduce a diagnostic to measure \emph{persistence} of community structure
in a multilayer network partition. We prove several results that describe how
the multilayer maximization problem measures a trade-off between static
community structure within layers and larger values of persistence across
layers. We also discuss some computational issues that the popular "Louvain"
heuristic faces with temporal multilayer networks and suggest ways to mitigate
them.Comment: 42 pages, many figures, final accepted version before typesettin
Seed selection for information cascade in multilayer networks
Information spreading is an interesting field in the domain of online social
media. In this work, we are investigating how well different seed selection
strategies affect the spreading processes simulated using independent cascade
model on eighteen multilayer social networks. Fifteen networks are built based
on the user interaction data extracted from Facebook public pages and tree of
them are multilayer networks downloaded from public repository (two of them
being Twitter networks). The results indicate that various state of the art
seed selection strategies for single-layer networks like K-Shell or VoteRank do
not perform so well on multilayer networks and are outperformed by Degree
Centrality
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
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