3,526 research outputs found
Node and layer eigenvector centralities for multiplex networks
Eigenvector-based centrality measures are among the most popular centrality measures in network science. The underlying idea is intuitive and the mathematical description is extremely simple in the framework of standard, mono-layer networks. Moreover, several efficient computational tools are available for their computation. Moving up in dimensionality, several efforts have been made in the past to describe an eigenvector-based entrality measure that generalizes the Bonacich index to the case of multiplex networks. In this work, we propose a new definition of eigenvector centrality that relies on the Perron eigenvector of a multi-homogeneous map defined in terms of the tensor describing the network. We prove that existence and uniqueness of such centrality are guaranteed under very mild assumptions on the multiplex network. Extensive numerical studies are proposed to test the newly introduced centrality measure and to compare it to other existing eigenvector-based centralities
MuxViz: A Tool for Multilayer Analysis and Visualization of Networks
Multilayer relationships among entities and information about entities must
be accompanied by the means to analyze, visualize, and obtain insights from
such data. We present open-source software (muxViz) that contains a collection
of algorithms for the analysis of multilayer networks, which are an important
way to represent a large variety of complex systems throughout science and
engineering. We demonstrate the ability of muxViz to analyze and interactively
visualize multilayer data using empirical genetic, neuronal, and transportation
networks. Our software is available at https://github.com/manlius/muxViz.Comment: 18 pages, 10 figures (text of the accepted manuscript
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
Opinion-Based Centrality in Multiplex Networks: A Convex Optimization Approach
Most people simultaneously belong to several distinct social networks, in
which their relations can be different. They have opinions about certain
topics, which they share and spread on these networks, and are influenced by
the opinions of other persons. In this paper, we build upon this observation to
propose a new nodal centrality measure for multiplex networks. Our measure,
called Opinion centrality, is based on a stochastic model representing opinion
propagation dynamics in such a network. We formulate an optimization problem
consisting in maximizing the opinion of the whole network when controlling an
external influence able to affect each node individually. We find a
mathematical closed form of this problem, and use its solution to derive our
centrality measure. According to the opinion centrality, the more a node is
worth investing external influence, and the more it is central. We perform an
empirical study of the proposed centrality over a toy network, as well as a
collection of real-world networks. Our measure is generally negatively
correlated with existing multiplex centrality measures, and highlights
different types of nodes, accordingly to its definition
The use of multilayer network analysis in animal behaviour
Network analysis has driven key developments in research on animal behaviour
by providing quantitative methods to study the social structures of animal
groups and populations. A recent formalism, known as \emph{multilayer network
analysis}, has advanced the study of multifaceted networked systems in many
disciplines. It offers novel ways to study and quantify animal behaviour as
connected 'layers' of interactions. In this article, we review common questions
in animal behaviour that can be studied using a multilayer approach, and we
link these questions to specific analyses. We outline the types of behavioural
data and questions that may be suitable to study using multilayer network
analysis. We detail several multilayer methods, which can provide new insights
into questions about animal sociality at individual, group, population, and
evolutionary levels of organisation. We give examples for how to implement
multilayer methods to demonstrate how taking a multilayer approach can alter
inferences about social structure and the positions of individuals within such
a structure. Finally, we discuss caveats to undertaking multilayer network
analysis in the study of animal social networks, and we call attention to
methodological challenges for the application of these approaches. Our aim is
to instigate the study of new questions about animal sociality using the new
toolbox of multilayer network analysis.Comment: Thoroughly revised; title changed slightl
- …