Detection of community structures in networks via global optimization

Medus, A. D.; Acuña, Gerardo; Dorso, C. O.

doi:10.1016/j.physa.2005.04.022

Cited by 151 publications

(118 citation statements)

References 14 publications

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“…An edge in the graph represents the simultaneous appearance of the corresponding characters in one or more chapters of the novel. The clusters obtained agree (with minor modifications) with those obtained with other methods, see for example [12].…”

Section: Real-life Networksupporting

confidence: 83%

A fast and efficient algorithm to identify clusters in networks

Comellas

Miralles

2010

Applied Mathematics and Computation

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A characteristic feature of many relevant real life networks, like the WWW, Internet, transportation and communication networks, or even biological and social networks, is their clustering structure. We discuss in this paper a novel algorithm to identify clusters -sets of densely interconnected nodesin a network. The algorithm is based on local information and therefore it is very fast with respect other proposed methods, while it keeps a similar performance in detecting the clusters.

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Section: Real-life Networksupporting

confidence: 83%

A fast and efficient algorithm to identify clusters in networks

Comellas

Miralles

2010

Applied Mathematics and Computation

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“…A variety of approximate techniques from physics and elsewhere, however, are applicable to the problem and seem to give good, but not perfect, solutions with relatively modest computational effort. These include simulated annealing 17,53 , greedy algorithms 54,55 , semidefinite programming 28 , spectral methods 56 and several others 40,57 . Modularity maximization forms the basis for other more complex approaches as well, such as the method of Blondel et al 27 , a multiscale method in which modularity is first optimized using a greedy local algorithm, then a 'supernetwork' is formed whose nodes represent the communities so discovered and the greedy algorithm is repeated on this supernetwork.…”

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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“…Many heuristics have been proposed, while exact algorithms for modularity maximization are rare. Heuristics are based on agglomerative hierarchical clustering [2][3][4][5][6], simulated annealing [7][8][9], mean field annealing [10], genetic search [11], extremal optimization [12], spectral clustering [13], linear programming followed by randomized rounding [14], dynamical clustering [15], multilevel partitioning [16], contraction-dilation [17], multistep greedy search [18], quantum mechanics [19] and many more [6,[20][21][22][23][24]. These heuristics are able to solve large instances with up to hundred or thousand entities and therefore are often preferred to exact algorithms, even though they do not have a guarantee of optimality.…”

Section: Introductionmentioning

confidence: 99%

Improving heuristics for network modularity maximization using an exact algorithm

Cafieri

Hansen

Liberti

2014

Discrete Applied Mathematics

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Abstract. Heuristics are widely applied to modularity maximization models for the identification of communities in complex networks. We present an approach to be applied as a post-processing on heuristic methods in order to improve their performances. Starting from a given partition, we test with an exact algorithm for bipartitioning if it is worthwhile to split some communities or to merge two of them. A combination of merge and split actions is also performed. Computational experiments show that the proposed approach is effective in improving heuristic results.

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Detection of community structures in networks via global optimization

Cited by 151 publications

References 14 publications

A fast and efficient algorithm to identify clusters in networks

A fast and efficient algorithm to identify clusters in networks

Communities, modules and large-scale structure in networks

Improving heuristics for network modularity maximization using an exact algorithm

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