Finding instabilities in the community structure of complex networks

Gfeller, David; Chappelier, Jean-Cédric; Rios, Paolo De Los

doi:10.1103/physreve.72.056135

Cited by 120 publications

(107 citation statements)

References 27 publications

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“…There may exist several but very different partitions that all have a comparably high value of modularity. Palla et al [25] have introduced an algorithm to detect overlapping communities by clique percolation and Gfeller et al have introduced the notion of nodes lying "between clusters" [26]. In the framework of this article, the overlap of communities is linked to the degeneracy of the minima of the Hamiltonian.…”

Section: Overlap and Stability Of Community Assignmentsmentioning

confidence: 99%

Statistical mechanics of community detection

2006

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Starting from a general ansatz, we show how community detection can be interpreted as finding the ground state of an infinite range spin glass. Our approach applies to weighted and directed networks alike. It contains the at hoc introduced quality function from [1] and the modularity Q as defined by Newman and Girvan [2] as special cases. The community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices. We elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study. Further we show, how hierarchies and overlap in the community structure can be detected. Computationally effective local update rules for optimization procedures to find the ground state are given. We show how the ansatz may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension. Finally, we give expectation values for the modularity of random graphs, which can be used in the assessment of statistical significance of community structure.

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Section: Overlap and Stability Of Community Assignmentsmentioning

confidence: 99%

Statistical mechanics of community detection

2006

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“…This is only one of the many ways in which different solutions can be aggregated. For other methods of aggregation used in community detection refer to [26,36,37]. Figure 8 shows the similarities between aggregate solutions.…”

Section: B Aggregatementioning

confidence: 99%

Near linear time algorithm to detect community structures in large-scale networks

2007

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Community detection and analysis is an important methodology for understanding the organization of various real-world networks and has applications in problems as diverse as consensus formation in social communities or the identification of functional modules in biochemical networks. Currently used algorithms that identify the community structures in large-scale real-world networks require a priori information such as the number and sizes of communities or are computationally expensive. In this paper we investigate a simple label propagation algorithm that uses the network structure alone as its guide and requires neither optimization of a pre-defined objective function nor prior information about the communities. In our algorithm every node is initialized with a unique label and at every step each node adopts the label that most of its neighbors currently have. In this iterative process densely connected groups of nodes form a consensus on a unique label to form communities. We validate the algorithm by applying it to networks whose community structures are known. We also demonstrate that the algorithm takes an almost linear time and hence it is computationally less expensive than what was possible so far.

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“…The robustness and uniqueness of a discovered partitioning is also examined in [Gfeller et al 2005;Karrer et al 2008;Massen and Doye 2007]. Many of these techniques can be extend to assess the overlapping community structure.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Overlapping community detection in networks

2013

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This paper reviews the state of the art in overlapping community detection algorithms, quality measures, and benchmarks. A thorough comparison of different algorithms (a total of fourteen) is provided. In addition to community level evaluation, we propose a framework for evaluating algorithms' ability to detect overlapping nodes, which helps to assess over-detection and underdetection. After considering community level detection performance measured by Normalized Mutual Information, the Omega index, and node level detection performance measured by Fscore, we reached the following conclusions. For low overlapping density networks, SLPA, OSLOM, Game and COPRA offer better performance than the other tested algorithms. For networks with high overlapping density and high overlapping diversity, both SLPA and Game provide relatively stable performance. However, test results also suggest that the detection in such networks is still not yet fully resolved. A common feature observed by various algorithms in real-world networks is the relatively small fraction of overlapping nodes (typically less than 30%), each of which belongs to only 2 or 3 communities.

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Finding instabilities in the community structure of complex networks

Cited by 120 publications

References 27 publications

Statistical mechanics of community detection

Statistical mechanics of community detection

Near linear time algorithm to detect community structures in large-scale networks

Overlapping community detection in networks

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