744 research outputs found
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
A Tensor-Based Framework for Studying Eigenvector Multicentrality in Multilayer Networks
Centrality is widely recognized as one of the most critical measures to
provide insight in the structure and function of complex networks. While
various centrality measures have been proposed for single-layer networks, a
general framework for studying centrality in multilayer networks (i.e.,
multicentrality) is still lacking. In this study, a tensor-based framework is
introduced to study eigenvector multicentrality, which enables the
quantification of the impact of interlayer influence on multicentrality,
providing a systematic way to describe how multicentrality propagates across
different layers. This framework can leverage prior knowledge about the
interplay among layers to better characterize multicentrality for varying
scenarios. Two interesting cases are presented to illustrate how to model
multilayer influence by choosing appropriate functions of interlayer influence
and design algorithms to calculate eigenvector multicentrality. This framework
is applied to analyze several empirical multilayer networks, and the results
corroborate that it can quantify the influence among layers and multicentrality
of nodes effectively.Comment: 57 pages, 10 figure
Interbank markets and multiplex networks: centrality measures and statistical null models
The interbank market is considered one of the most important channels of
contagion. Its network representation, where banks and claims/obligations are
represented by nodes and links (respectively), has received a lot of attention
in the recent theoretical and empirical literature, for assessing systemic risk
and identifying systematically important financial institutions. Different
types of links, for example in terms of maturity and collateralization of the
claim/obligation, can be established between financial institutions. Therefore
a natural representation of the interbank structure which takes into account
more features of the market, is a multiplex, where each layer is associated
with a type of link. In this paper we review the empirical structure of the
multiplex and the theoretical consequences of this representation. We also
investigate the betweenness and eigenvector centrality of a bank in the
network, comparing its centrality properties across different layers and with
Maximum Entropy null models.Comment: To appear in the book "Interconnected Networks", A. Garas e F.
Schweitzer (eds.), Springer Complexity Serie
Distance entropy cartography characterises centrality in complex networks
We introduce distance entropy as a measure of homogeneity in the distribution
of path lengths between a given node and its neighbours in a complex network.
Distance entropy defines a new centrality measure whose properties are
investigated for a variety of synthetic network models. By coupling distance
entropy information with closeness centrality, we introduce a network
cartography which allows one to reduce the degeneracy of ranking based on
closeness alone. We apply this methodology to the empirical multiplex lexical
network encoding the linguistic relationships known to English speaking
toddlers. We show that the distance entropy cartography better predicts how
children learn words compared to closeness centrality. Our results highlight
the importance of distance entropy for gaining insights from distance patterns
in complex networks.Comment: 11 page
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