2,734 research outputs found
Sandpiles on multiplex networks
We introduce the sandpile model on multiplex networks with more than one type
of edge and investigate its scaling and dynamical behaviors. We find that the
introduction of multiplexity does not alter the scaling behavior of avalanche
dynamics; the system is critical with an asymptotic power-law avalanche size
distribution with an exponent on duplex random networks. The
detailed cascade dynamics, however, is affected by the multiplex coupling. For
example, higher-degree nodes such as hubs in scale-free networks fail more
often in the multiplex dynamics than in the simplex network counterpart in
which different types of edges are simply aggregated. Our results suggest that
multiplex modeling would be necessary in order to gain a better understanding
of cascading failure phenomena of real-world multiplex complex systems, such as
the global economic crisis.Comment: 7 pages, 7 figure
Structure of Triadic Relations in Multiplex Networks
Recent advances in the study of networked systems have highlighted that our
interconnected world is composed of networks that are coupled to each other
through different "layers" that each represent one of many possible subsystems
or types of interactions. Nevertheless, it is traditional to aggregate
multilayer networks into a single weighted network in order to take advantage
of existing tools. This is admittedly convenient, but it is also extremely
problematic, as important information can be lost as a result. It is therefore
important to develop multilayer generalizations of network concepts. In this
paper, we analyze triadic relations and generalize the idea of transitivity to
multiplex networks. By focusing on triadic relations, which yield the simplest
type of transitivity, we generalize the concept and computation of clustering
coefficients to multiplex networks. We show how the layered structure of such
networks introduces a new degree of freedom that has a fundamental effect on
transitivity. We compute multiplex clustering coefficients for several real
multiplex networks and illustrate why one must take great care when
generalizing standard network concepts to multiplex networks. We also derive
analytical expressions for our clustering coefficients for ensemble averages of
networks in a family of random multiplex networks. Our analysis illustrates
that social networks have a strong tendency to promote redundancy by closing
triads at every layer and that they thereby have a different type of multiplex
transitivity from transportation networks, which do not exhibit such a
tendency. These insights are invisible if one only studies aggregated networks.Comment: Main text + Supplementary Material included in a single file.
Published in New Journal of Physic
Relay synchronization in multiplex networks
Relay (or remote) synchronization between two not directly connected
oscillators in a network is an important feature allowing distant coordination.
In this work, we report a systematic study of this phenomenon in multiplex
networks, where inter-layer synchronization occurs between distant layers
mediated by a relay layer that acts as a transmitter. We show that this
transmission can be extended to higher order relay configurations, provided
symmetry conditions are preserved. By first order perturbative analysis, we
identify the dynamical and topological dependencies of relay synchronization in
a multiplex. We find that the relay synchronization threshold is considerably
reduced in a multiplex configuration, and that such synchronous state is mostly
supported by the lower degree nodes of the outer layers, while hubs can be
de-multiplexed without affecting overall coherence. Finally, we experimentally
validated the analytical and numerical findings by means of a multiplex of
three layers of electronic circuits.the analytical and numerical findings by
means of a multiplex of three layers of electronic circuits
Optimization of synchronizability in multiplex networks
We investigate the optimization of synchronizability in multiplex networks
and demonstrate that the interlayer coupling strength is the deciding factor
for the efficiency of optimization. The optimized networks have homogeneity in
the degree as well as in the betweenness centrality. Additionally, the
interlayer coupling strength crucially affects various properties of individual
layers in the optimized multiplex networks. We provide an understanding to how
the emerged network properties are shaped or affected when the evolution
renders them better synchronizable.Comment: 6 pages and 6 figure
- …