1,322 research outputs found
Multiple structural transitions in interacting networks
Many real-world systems can be modeled as interconnected multilayer networks,
namely a set of networks interacting with each other. Here we present a
perturbative approach to study the properties of a general class of
interconnected networks as inter-network interactions are established. We
reveal multiple structural transitions for the algebraic connectivity of such
systems, between regimes in which each network layer keeps its independent
identity or drives diffusive processes over the whole system, thus generalizing
previous results reporting a single transition point. Furthermore we show that,
at first order in perturbation theory, the growth of the algebraic connectivity
of each layer depends only on the degree configuration of the interaction
network (projected on the respective Fiedler vector), and not on the actual
interaction topology. Our findings can have important implications in the
design of robust interconnected networked system, particularly in the presence
of network layers whose integrity is more crucial for the functioning of the
entire system. We finally show results of perturbation theory applied to the
adjacency matrix of the interconnected network, which can be useful to
characterize percolation processes on such systems
Layer degradation triggers an abrupt structural transition in multiplex networks
Network robustness is a central point in network science, both from a
theoretical and a practical point of view. In this paper, we show that layer
degradation, understood as the continuous or discrete loss of links' weight,
triggers a structural transition revealed by an abrupt change in the algebraic
connectivity of the graph. Unlike traditional single layer networks, multiplex
networks exist in two phases, one in which the system is protected from link
failures in some of its layers and one in which all the system senses the
failure happening in one single layer. We also give the exact critical value of
the weight of the intra-layer links at which the transition occurs for
continuous layer degradation and its relation to the value of the coupling
between layers. This relation allows us to reveal the connection between the
transition observed under layer degradation and the one observed under the
variation of the coupling between layers.Comment: 8 pages, and 8 figures in Revtex style. Submitted for publicatio
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
Abrupt transition in the structural formation of interconnected networks
Our current world is linked by a complex mesh of networks where information,
people and goods flow. These networks are interdependent each other, and
present structural and dynamical features different from those observed in
isolated networks. While examples of such "dissimilar" properties are becoming
more abundant, for example diffusion, robustness and competition, it is not yet
clear where these differences are rooted in. Here we show that the composition
of independent networks into an interconnected network of networks undergoes a
structurally sharp transition as the interconnections are formed. Depending of
the relative importance of inter and intra-layer connections, we find that the
entire interdependent system can be tuned between two regimes: in one regime,
the various layers are structurally decoupled and they act as independent
entities; in the other regime, network layers are indistinguishable and the
whole system behave as a single-level network. We analytically show that the
transition between the two regimes is discontinuous even for finite size
networks. Thus, any real-world interconnected system is potentially at risk of
abrupt changes in its structure that may reflect in new dynamical properties.Comment: 10 pages, 3 figure
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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