Analysis of the structure of complex networks at different resolution levels

Arenas, Àlex; Fernández, Alberto; Gómez, Sergio

doi:10.1088/1367-2630/10/5/053039

Cited by 464 publications

(551 citation statements)

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“…In particular, it has a known bias in the size of the communities it finds-it has a preference for communities of size roughly equal to the square root of the size of the network 58 . Modifications of the method have been proposed that allow one to vary this preferred size 59,60 , but not to eliminate the preference altogether. The modularity method also ignores any information stored in the positions of edges that run between communities: as modularity is calculated by counting only within-group edges, one could move the between-group edges around in any way one pleased and the value of the modularity would not change at all.…”

Section: Optimization Methodsmentioning

confidence: 99%

Communities, modules and large-scale structure in networks

2011

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Networks, also called graphs by mathematicians, provide a useful abstraction of the structure of many complex systems, ranging from social systems and computer networks to biological networks and the state spaces of physical systems. In the past decade there have been significant advances in experiments to determine the topological structure of networked systems, but there remain substantial challenges in extracting scientific understanding from the large quantities of data produced by the experiments. A variety of basic measures and metrics are available that can tell us about small-scale structure in networks, such as correlations, connections and recurrent patterns, but it is considerably more difficult to quantify structure on medium and large scales, to understand the 'big picture'. Important progress has been made, however, within the past few years, a selection of which is reviewed here.A network is, in its simplest form, a collection of dots joined together in pairs by lines (Fig. 1). In the jargon of the field, a dot is called a 'node' or 'vertex' (plural 'vertices') and a line is called an 'edge'. Networks are used in many branches of science as a way to represent the patterns of connections between the components of complex systems [1][2][3][4][5][6] . Examples include the Internet 7,8 , in which the nodes are computers and the edges are data connections such as optical-fibre cables, food webs in biology 9,10 , in which the nodes are species in an ecosystem and the edges represent predator-prey interactions, and social networks 11,12 , in which the nodes are people and the edges represent any of a variety of different types of social interaction including friendship, collaboration, business relationships or others.In the past decade there has been a surge of interest in both empirical studies of networks 13 and development of mathematical and computational tools for extracting insight from network data 1-6 . One common approach to the study of networks is to focus on the properties of individual nodes or small groups of nodes, asking questions such as, 'Which is the most important node in this network?' or 'Which are the strongest connections?' Such approaches, however, tell us little about large-scale network structure. It is this large-scale structure that is the topic of this paper.The best-studied form of large-scale structure in networks is modular or community structure 14,15 . A community, in this context, is a dense subnetwork within a larger network, such as a close-knit group of friends in a social network or a group of interlinked web pages on the World Wide Web (Fig. 1). Although communities are not the only interesting form of large-scale structure-there are others that we will come to-they serve as a good illustration of the nature and scope of present research in this area and will be our primary focus.Communities are of interest for a number of reasons. They have intrinsic interest because they may correspond to functional units within a networked system, an example of the kind of link...

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Section: Optimization Methodsmentioning

confidence: 99%

Communities, modules and large-scale structure in networks

2011

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“…As Figure 2(a) shows, our method using the global criteria can process such network in 132 s to 409 s (depending on the criterion) across 100 scales, which for comparison can be brought to an average of about 1.32 s to 4.09 s per scale. The global criteria from [6,7,8] were introduced and studied for their analysis performance. They were optimised using modified versions of the fast Newman algorithm [15], significantly outperformed in speed by the Louvain method.…”

Section: Comparison With Related Workmentioning

confidence: 99%

“…Several criteria designed for multi-scale analysis have been presented in [6,7,8,9,10]. However no efficient method to uncover communities across scales was suggested.…”

Section: Introductionmentioning

confidence: 99%

“…The two best known are probably variations of Newman's modularity [15] by Reichardt and Bornholdt [6] and Arenas et al [7].…”

Section: Introductionmentioning

confidence: 99%

“…It is optimised in a global manner though.) The first two methods from Reichardt and Bornholdt [6] and Arenas et al [7] somewhat share the idea that modifying the impact of some factors within the modularity equation (e.g. the null factor, nodes weight with self-loops) can offer a multi-scale approach to community detection using modularity.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fast Multi-Scale Detection of Relevant Communities in Large-Scale Networks

Martelot

Hankin

2013

The Computer Journal

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Nowadays, networks are almost ubiquitous. In the past decade, community detection received an increasing interest as a way to uncover the structure of networks by grouping nodes into communities more densely connected internally than externally. Yet most of the effective methods available do not consider the potential levels of organisation, or scales, a network may encompass and are therefore limited. In this paper we present a method compatible with global and local criteria that enables fast multi-scale community detection on large networks. The method is derived in two algorithms, one for each type of criterion, and implemented with 6 known criteria. Uncovering communities at various scales is a computationally expensive task. Therefore this work puts a strong emphasis on the reduction of computational complexity. Some heuristics are introduced for speed-up purposes. Experiments demonstrate the efficiency and accuracy of our method with respect to each algorithm and criterion by testing them against large generated multi-scale networks. This study also offers a comparison between criteria and between the global and local approaches. In particular our results suggest that global criteria seem to be more robust to noise and thus more accurate than local criteria.

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