2,137 research outputs found
Cascading failures in coupled networks with both inner-dependency and inter-dependency links
We study the percolation in coupled networks with both inner-dependency and
inter-dependency links, where the inner- and inter-dependency links represent
the dependencies between nodes in the same or different networks, respectively.
We find that when most of dependency links are inner- or inter-ones, the
coupled networks system is fragile and makes a discontinuous percolation
transition. However, when the numbers of two types of dependency links are
close to each other, the system is robust and makes a continuous percolation
transition. This indicates that the high density of dependency links could not
always lead to a discontinuous percolation transition as the previous studies.
More interestingly, although the robustness of the system can be optimized by
adjusting the ratio of the two types of dependency links, there exists a
critical average degree of the networks for coupled random networks, below
which the crossover of the two types of percolation transitions disappears, and
the system will always demonstrate a discontinuous percolation transition. We
also develop an approach to analyze this model, which is agreement with the
simulation results well.Comment: 9 pages, 4 figure
Percolation Theory on Interdependent Networks Based on Epidemic Spreading
We consider percolation on interdependent locally treelike networks, recently
introduced by Buldyrev et al., Nature 464, 1025 (2010), and demonstrate that
the problem can be simplified conceptually by deleting all references to
cascades of failures. Such cascades do exist, but their explicit treatment just
complicates the theory -- which is a straightforward extension of the usual
epidemic spreading theory on a single network. Our method has the added
benefits that it is directly formulated in terms of an order parameter and its
modular structure can be easily extended to other problems, e.g. to any number
of interdependent networks, or to networks with dependency links.Comment: 6 pages, 5 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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