Community landscapes: an integrative approach to determine overlapping network module hierarchy, identify key nodes and predict network dynamics
📝 Abstract
Background: Network communities help the functional organization and evolution of complex networks. However, the development of a method, which is both fast and accurate, provides modular overlaps and partitions of a heterogeneous network, has proven to be rather difficult. Methodology/Principal Findings: Here we introduce the novel concept of ModuLand, an integrative method family determining overlapping network modules as hills of an influence function-based, centrality-type community landscape, and including several widely used modularization methods as special cases. As various adaptations of the method family, we developed several algorithms, which provide an efficient analysis of weighted and directed networks, and (1) determine pervasively overlapping modules with high resolution; (2) uncover a detailed hierarchical network structure allowing an efficient, zoom-in analysis of large networks; (3) allow the determination of key network nodes and (4) help to predict network dynamics. Conclusions/Significance: The concept opens a wide range of possibilities to develop new approaches and applications including network routing, classification, comparison and prediction.
💡 Analysis
Background: Network communities help the functional organization and evolution of complex networks. However, the development of a method, which is both fast and accurate, provides modular overlaps and partitions of a heterogeneous network, has proven to be rather difficult. Methodology/Principal Findings: Here we introduce the novel concept of ModuLand, an integrative method family determining overlapping network modules as hills of an influence function-based, centrality-type community landscape, and including several widely used modularization methods as special cases. As various adaptations of the method family, we developed several algorithms, which provide an efficient analysis of weighted and directed networks, and (1) determine pervasively overlapping modules with high resolution; (2) uncover a detailed hierarchical network structure allowing an efficient, zoom-in analysis of large networks; (3) allow the determination of key network nodes and (4) help to predict network dynamics. Conclusions/Significance: The concept opens a wide range of possibilities to develop new approaches and applications including network routing, classification, comparison and prediction.
📄 Content
1 PLoS ONE 5, e12528 (2010)
Community landscapes: an integrative approach to determine overlapping network module hierarchy, identify key nodes and predict network dynamics
István A. Kovács1,2, Robin Palotai1, Máté S. Szalay1, Peter Csermely1,*
1Department of Medical Chemistry, Semmelweis University, Budapest, Hungary 2Department of Physics, Loránd Eötvös University, Budapest, Hungary *Corresponding author; Department of Medical Chemistry, Semmelweis University, P.O.Box 260, H-1444 Budapest 8, Hungary; Tel: +36-1-459-1500/60130; E-mail: csermely@eok.sote.hu
Background: Network communities help the functional organization and evolution of
complex networks. However, the development of a method, which is both fast and
accurate, provides modular overlaps and partitions of a heterogeneous network, has
proven to be rather difficult.
Methodology/Principal Findings: Here we introduce the novel concept of ModuLand,
an integrative method family determining overlapping network modules as hills of an
influence function-based, centrality-type community landscape, and including several
widely used modularization methods as special cases. As various adaptations of the
method family, we developed several algorithms, which provide an efficient analysis of
weighted and directed networks, and (1) determine pervasively overlapping modules with
high resolution; (2) uncover a detailed hierarchical network structure allowing an
efficient, zoom-in analysis of large networks; (3) allow the determination of key network
nodes and (4) help to predict network dynamics.
Conclusions/Significance: The concept opens a wide range of possibilities to develop
new approaches and applications including network routing, classification, comparison
and prediction.
Introduction
In real networks, module or community structure plays a central role in the understanding of topology and dynamics. Numerous module determination methods are based on the intuitive picture identifying the network communities as dense groups of the network, whose nodes have a much stronger influence on each other than on the rest of the network. The development of a method, which translates this intuitive definition of modules into a practically applicable, fast, accurate and widely usable algorithm turned out to be a very challenging problem. So far a wide variety of great ideas and powerful approaches based on very different physical or algorithmic grounds were applied in order to solve this problem. At the moment there is no ‘best method’ available to find network modules, and even the widely used algorithms may suffer from serious problems (see Figure S1.1, and Tables S1.1 and S1.2 in the Electronic Supplementary Material S1) [1- 7], although they usually provide useful and clear dissections of networks.
2 In 2002 Girvan and Newman published a seminal paper [2] using an algorithm for detecting communities by iteratively removing edges of high betweenness centrality values from the network, and defining communities as the connected components of the network after these edge removals. Later they [8] introduced the modularity measure, Q with which the optimal number of removed edges could be determined. In a short time the Q function evaluating the goodness of partitioning a graph into given clusters became an essential element of a wide range of clustering methods. Different kind of approaches have also been developed, including ones utilizing spectral functions of the graphs [9,10], dynamic algorithms like random walks [5,11], spin models (e.g. the Potts model) [12] or synchronization models [13]. The most popular method to find overlapping communities is the Clique Percolation Method described by Palla et al. in [7], but other excellent methods optimizing overlapping quality functions such as that of Nepusz et al. [4] or the link-based method resulting in pervasive overlaps [14] also exist. Although the field of community detection is quite diversified, we tried to collect the main algorithms in Table S1.2 in the Electronic Supplementary Material S1, and we also recommend a current extensive review of the field by Santo Fortunato [1].
In this paper we introduce an integrative network module determination method family, called ModuLand (see Box 1 for the glossary of novel terms). This module determination method family is based on the novel concept of understanding the overlapping modules as hills of an influence function-based, centrality-type community landscape. The ModuLand method family gives a common framework for the development and comparison of a large variety of modularization methods resulting in network modules with variable overlaps, requiring different computational speed and providing a different level of accuracy.
Results
Description of the ModuLand method family
Keeping in mind the emerging needs for an integrative approach for the determination of network modules,
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