1,246 research outputs found
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
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The social and economic bases of network multiplexity: Exploring the emergence of multiplex ties
The goal of this article is to shed light on the role of tie content in the evolution of multiplex ties – i.e., ties featuring both an economic and a social component – in interorganizational networks. The authors clarify and extend the theoretical framework on network multiplexity by testing the extent to which two distinct tie content-related logics – social interaction and economic exchange – and their underlying mechanisms lead to the emergence of multiplex ties. Results from a longitudinal network analysis of firms located in an Italian multimedia cluster support the authors’ hypotheses, confirming that both social and economic drivers contribute to the emergence of network multiplexity, and that social ties have a stronger impact than economic ties on this process, thus providing further insight into the microdynamics of network evolution
Layer-switching cost and optimality in information spreading on multiplex networks
We study a model of information spreading on multiplex networks, in which
agents interact through multiple interaction channels (layers), say online vs.\
offline communication layers, subject to layer-switching cost for transmissions
across different interaction layers. The model is characterized by the
layer-wise path-dependent transmissibility over a contact, that is dynamically
determined dependently on both incoming and outgoing transmission layers. We
formulate an analytical framework to deal with such path-dependent
transmissibility and demonstrate the nontrivial interplay between the
multiplexity and spreading dynamics, including optimality. It is shown that the
epidemic threshold and prevalence respond to the layer-switching cost
non-monotonically and that the optimal conditions can change in abrupt
non-analytic ways, depending also on the densities of network layers and the
type of seed infections. Our results elucidate the essential role of
multiplexity that its explicit consideration should be crucial for realistic
modeling and prediction of spreading phenomena on multiplex social networks in
an era of ever-diversifying social interaction layers.Comment: 15 pages, 7 figure
Joint effect of ageing and multilayer structure prevents ordering in the voter model
The voter model rules are simple, with agents copying the state of a random
neighbor, but they lead to non-trivial dynamics. Besides opinion processes, the
model has also applications for catalysis and species competition. Inspired by
the temporal inhomogeneities found in human interactions, one can introduce
ageing in the agents: the probability to update decreases with the time elapsed
since the last change. This modified dynamics induces an approach to consensus
via coarsening in complex networks. Additionally, multilayer networks produce
profound changes in the dynamics of models. In this work, we investigate how a
multilayer structure affects the dynamics of an ageing voter model. The system
is studied as a function of the fraction of nodes sharing states across layers
(multiplexity parameter q ). We find that the dynamics of the system suffers a
notable change at an intermediate value q*. Above it, the voter model always
orders to an absorbing configuration. While, below, a fraction of the
realizations falls into dynamical traps associated to a spontaneous symmetry
breaking in which the majority opinion in the different layers takes opposite
signs and that due to the ageing indefinitely delay the arrival at the
absorbing state.Comment: 10 pages, 8 figure
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
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