2,521 research outputs found
Community detection in complex networks by dynamical simplex evolution
We benchmark the dynamical simplex evolution (DSE) method with several of the currently available algorithms to detect communities in complex networks by comparing correctly identified nodes for different levels of fuzziness of random networks composed of well-defined communities. The potential benefits of the DSE method to detect hierarchical substructures in complex networks are discussed
Persistent homology of time-dependent functional networks constructed from coupled time series
We use topological data analysis to study "functional networks" that we
construct from time-series data from both experimental and synthetic sources.
We use persistent homology with a weight rank clique filtration to gain
insights into these functional networks, and we use persistence landscapes to
interpret our results. Our first example uses time-series output from networks
of coupled Kuramoto oscillators. Our second example consists of biological data
in the form of functional magnetic resonance imaging (fMRI) data that was
acquired from human subjects during a simple motor-learning task in which
subjects were monitored on three days in a five-day period. With these
examples, we demonstrate that (1) using persistent homology to study functional
networks provides fascinating insights into their properties and (2) the
position of the features in a filtration can sometimes play a more vital role
than persistence in the interpretation of topological features, even though
conventionally the latter is used to distinguish between signal and noise. We
find that persistent homology can detect differences in synchronization
patterns in our data sets over time, giving insight both on changes in
community structure in the networks and on increased synchronization between
brain regions that form loops in a functional network during motor learning.
For the motor-learning data, persistence landscapes also reveal that on average
the majority of changes in the network loops take place on the second of the
three days of the learning process.Comment: 17 pages (+3 pages in Supplementary Information), 11 figures in many
text (many with multiple parts) + others in SI, submitte
MuxViz: A Tool for Multilayer Analysis and Visualization of Networks
Multilayer relationships among entities and information about entities must
be accompanied by the means to analyze, visualize, and obtain insights from
such data. We present open-source software (muxViz) that contains a collection
of algorithms for the analysis of multilayer networks, which are an important
way to represent a large variety of complex systems throughout science and
engineering. We demonstrate the ability of muxViz to analyze and interactively
visualize multilayer data using empirical genetic, neuronal, and transportation
networks. Our software is available at https://github.com/manlius/muxViz.Comment: 18 pages, 10 figures (text of the accepted manuscript
Detection of hidden structures on all scales in amorphous materials and complex physical systems: basic notions and applications to networks, lattice systems, and glasses
Recent decades have seen the discovery of numerous complex materials. At the
root of the complexity underlying many of these materials lies a large number
of possible contending atomic- and larger-scale configurations and the
intricate correlations between their constituents. For a detailed
understanding, there is a need for tools that enable the detection of pertinent
structures on all spatial and temporal scales. Towards this end, we suggest a
new method by invoking ideas from network analysis and information theory. Our
method efficiently identifies basic unit cells and topological defects in
systems with low disorder and may analyze general amorphous structures to
identify candidate natural structures where a clear definition of order is
lacking. This general unbiased detection of physical structure does not require
a guess as to which of the system properties should be deemed as important and
may constitute a natural point of departure for further analysis. The method
applies to both static and dynamic systems.Comment: (23 pages, 9 figures
Simplicial complexes and complex systems
© 2018 European Physical Society. We provide a short introduction to the field of topological data analysis (TDA) and discuss its possible relevance for the study of complex systems. TDA provides a set of tools to characterise the shape of data, in terms of the presence of holes or cavities between the points. The methods, based on the notion of simplicial complexes, generalise standard network tools by naturally allowing for many-body interactions and providing results robust under continuous deformations of the data. We present strengths and weaknesses of current methods, as well as a range of empirical studies relevant to the field of complex systems, before identifying future methodological challenges to help understand the emergence of collective phenomena
A generalized simplicial model and its application
Higher-order structures, consisting of more than two individuals, provide a
new perspective to reveal the missed non-trivial characteristics under pairwise
networks. Prior works have researched various higher-order networks, but
research for evaluating the effects of higher-order structures on network
functions is still scarce. In this paper, we propose a framework to quantify
the effects of higher-order structures (e.g., 2-simplex) and vital functions of
complex networks by comparing the original network with its simplicial model.
We provide a simplicial model that can regulate the quantity of 2-simplices and
simultaneously fix the degree sequence. Although the algorithm is proposed to
control the quantity of 2-simplices, results indicate it can also indirectly
control simplexes more than 2-order. Experiments on spreading dynamics, pinning
control, network robustness, and community detection have shown that regulating
the quantity of 2-simplices changes network performance significantly. In
conclusion, the proposed framework is a general and effective tool for linking
higher-order structures with network functions. It can be regarded as a
reference object in other applications and can deepen our understanding of the
correlation between micro-level network structures and global network
functions
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