84,413 research outputs found
The map equation
Many real-world networks are so large that we must simplify their structure
before we can extract useful information about the systems they represent. As
the tools for doing these simplifications proliferate within the network
literature, researchers would benefit from some guidelines about which of the
so-called community detection algorithms are most appropriate for the
structures they are studying and the questions they are asking. Here we show
that different methods highlight different aspects of a network's structure and
that the the sort of information that we seek to extract about the system must
guide us in our decision. For example, many community detection algorithms,
including the popular modularity maximization approach, infer module
assignments from an underlying model of the network formation process. However,
we are not always as interested in how a system's network structure was formed,
as we are in how a network's extant structure influences the system's behavior.
To see how structure influences current behavior, we will recognize that links
in a network induce movement across the network and result in system-wide
interdependence. In doing so, we explicitly acknowledge that most networks
carry flow. To highlight and simplify the network structure with respect to
this flow, we use the map equation. We present an intuitive derivation of this
flow-based and information-theoretic method and provide an interactive on-line
application that anyone can use to explore the mechanics of the map equation.
We also describe an algorithm and provide source code to efficiently decompose
large weighted and directed networks based on the map equation.Comment: 9 pages and 3 figures, corrected typos. For associated Flash
application, see http://www.tp.umu.se/~rosvall/livemod/mapequation
Multilevel compression of random walks on networks reveals hierarchical organization in large integrated systems
To comprehend the hierarchical organization of large integrated systems, we
introduce the hierarchical map equation, which reveals multilevel structures in
networks. In this information-theoretic approach, we exploit the duality
between compression and pattern detection; by compressing a description of a
random walker as a proxy for real flow on a network, we find regularities in
the network that induce this system-wide flow. Finding the shortest multilevel
description of the random walker therefore gives us the best hierarchical
clustering of the network, the optimal number of levels and modular partition
at each level, with respect to the dynamics on the network. With a novel search
algorithm, we extract and illustrate the rich multilevel organization of
several large social and biological networks. For example, from the global air
traffic network we uncover countries and continents, and from the pattern of
scientific communication we reveal more than 100 scientific fields organized in
four major disciplines: life sciences, physical sciences, ecology and earth
sciences, and social sciences. In general, we find shallow hierarchical
structures in globally interconnected systems, such as neural networks, and
rich multilevel organizations in systems with highly separated regions, such as
road networks.Comment: 11 pages, 5 figures. For associated code, see
http://www.tp.umu.se/~rosvall/code.htm
ModuLand plug-in for Cytoscape: determination of hierarchical layers of overlapping network modules and community centrality
Summary: The ModuLand plug-in provides Cytoscape users an algorithm for
determining extensively overlapping network modules. Moreover, it identifies
several hierarchical layers of modules, where meta-nodes of the higher
hierarchical layer represent modules of the lower layer. The tool assigns
module cores, which predict the function of the whole module, and determines
key nodes bridging two or multiple modules. The plug-in has a detailed
JAVA-based graphical interface with various colouring options. The ModuLand
tool can run on Windows, Linux, or Mac OS. We demonstrate its use on protein
structure and metabolic networks. Availability: The plug-in and its user guide
can be downloaded freely from: http://www.linkgroup.hu/modules.php. Contact:
[email protected] Supplementary information: Supplementary
information is available at Bioinformatics online.Comment: 39 pages, 1 figure and a Supplement with 9 figures and 10 table
Complex networks: new trends for the analysis of brain connectivity
Today, the human brain can be studied as a whole. Electroencephalography,
magnetoencephalography, or functional magnetic resonance imaging techniques
provide functional connectivity patterns between different brain areas, and
during different pathological and cognitive neuro-dynamical states. In this
Tutorial we review novel complex networks approaches to unveil how brain
networks can efficiently manage local processing and global integration for the
transfer of information, while being at the same time capable of adapting to
satisfy changing neural demands.Comment: Tutorial paper to appear in the Int. J. Bif. Chao
Identifying modular flows on multilayer networks reveals highly overlapping organization in social systems
Unveiling the community structure of networks is a powerful methodology to
comprehend interconnected systems across the social and natural sciences. To
identify different types of functional modules in interaction data aggregated
in a single network layer, researchers have developed many powerful methods.
For example, flow-based methods have proven useful for identifying modular
dynamics in weighted and directed networks that capture constraints on flow in
the systems they represent. However, many networked systems consist of agents
or components that exhibit multiple layers of interactions. Inevitably,
representing this intricate network of networks as a single aggregated network
leads to information loss and may obscure the actual organization. Here we
propose a method based on compression of network flows that can identify
modular flows in non-aggregated multilayer networks. Our numerical experiments
on synthetic networks show that the method can accurately identify modules that
cannot be identified in aggregated networks or by analyzing the layers
separately. We capitalize on our findings and reveal the community structure of
two multilayer collaboration networks: scientists affiliated to the Pierre
Auger Observatory and scientists publishing works on networks on the arXiv.
Compared to conventional aggregated methods, the multilayer method reveals
smaller modules with more overlap that better capture the actual organization
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