7,508 research outputs found
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
On the complexity of color-avoiding site and bond percolation
The mathematical analysis of robustness and error-tolerance of complex
networks has been in the center of research interest. On the other hand, little
work has been done when the attack-tolerance of the vertices or edges are not
independent but certain classes of vertices or edges share a mutual
vulnerability. In this study, we consider a graph and we assign colors to the
vertices or edges, where the color-classes correspond to the shared
vulnerabilities. An important problem is to find robustly connected vertex
sets: nodes that remain connected to each other by paths providing any type of
error (i.e. erasing any vertices or edges of the given color). This is also
known as color-avoiding percolation. In this paper, we study various possible
modeling approaches of shared vulnerabilities, we analyze the computational
complexity of finding the robustly (color-avoiding) connected components. We
find that the presented approaches differ significantly regarding their
complexity.Comment: 14 page
Graph Summarization
The continuous and rapid growth of highly interconnected datasets, which are
both voluminous and complex, calls for the development of adequate processing
and analytical techniques. One method for condensing and simplifying such
datasets is graph summarization. It denotes a series of application-specific
algorithms designed to transform graphs into more compact representations while
preserving structural patterns, query answers, or specific property
distributions. As this problem is common to several areas studying graph
topologies, different approaches, such as clustering, compression, sampling, or
influence detection, have been proposed, primarily based on statistical and
optimization methods. The focus of our chapter is to pinpoint the main graph
summarization methods, but especially to focus on the most recent approaches
and novel research trends on this topic, not yet covered by previous surveys.Comment: To appear in the Encyclopedia of Big Data Technologie
Symmetry in Critical Random Boolean Network Dynamics
Using Boolean networks as prototypical examples, the role of symmetry in the
dynamics of heterogeneous complex systems is explored. We show that symmetry of
the dynamics, especially in critical states, is a controlling feature that can
be used both to greatly simplify analysis and to characterize different types
of dynamics. Symmetry in Boolean networks is found by determining the frequency
at which the various Boolean output functions occur. There are classes of
functions that consist of Boolean functions that behave similarly. These
classes are orbits of the controlling symmetry group. We find that the symmetry
that controls the critical random Boolean networks is expressed through the
frequency by which output functions are utilized by nodes that remain active on
dynamical attractors. This symmetry preserves canalization, a form of network
robustness. We compare it to a different symmetry known to control the dynamics
of an evolutionary process that allows Boolean networks to organize into a
critical state. Our results demonstrate the usefulness and power of using the
symmetry of the behavior of the nodes to characterize complex network dynamics,
and introduce a novel approach to the analysis of heterogeneous complex
systems
GraphStream: A Tool for bridging the gap between Complex Systems and Dynamic Graphs
The notion of complex systems is common to many domains, from Biology to
Economy, Computer Science, Physics, etc. Often, these systems are made of sets
of entities moving in an evolving environment. One of their major
characteristics is the emergence of some global properties stemmed from local
interactions between the entities themselves and between the entities and the
environment. The structure of these systems as sets of interacting entities
leads researchers to model them as graphs. However, their understanding
requires most often to consider the dynamics of their evolution. It is indeed
not relevant to study some properties out of any temporal consideration. Thus,
dynamic graphs seem to be a very suitable model for investigating the emergence
and the conservation of some properties. GraphStream is a Java-based library
whose main purpose is to help researchers and developers in their daily tasks
of dynamic problem modeling and of classical graph management tasks: creation,
processing, display, etc. It may also be used, and is indeed already used, for
teaching purpose. GraphStream relies on an event-based engine allowing several
event sources. Events may be included in the core of the application, read from
a file or received from an event handler
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