Narrow scope for resolution-limit-free community detection

Traag, Vincent; Dooren, Paul Van; Nesterov, Yurii

doi:10.1103/physreve.84.016114

Cited by 304 publications

(311 citation statements)

References 33 publications

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“…In this framework, the temporal resolution parameter x provides a means of tuning the number of communities discovered across layers: high values of x yield fewer communities, and low values yield more communities. It is beneficial to study a range of parameter values to examine the breadth of structural (i.e., intra-layer 24,25,71 ) and temporal (i.e., interlayer) resolutions of community structure, and some papers have begun to make progress in this direction. 3,4,13,31,72 To characterize community structure as a function of resolution-parameter values (and hence of system scales), we quantify the quality of partitions using the mean value of optimized Q.…”

Section: Structural and Temporal Resolution Parametersmentioning

confidence: 99%

Robust detection of dynamic community structure in networks

Bassett

Porter

Wymbs

et al. 2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

484

645

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We describe techniques for the robust detection of community structure in some classes of timedependent networks. Specifically, we consider the use of statistical null models for facilitating the principled identification of structural modules in semi-decomposable systems. Null models play an important role both in the optimization of quality functions such as modularity and in the subsequent assessment of the statistical validity of identified community structure. We examine the sensitivity of such methods to model parameters and show how comparisons to null models can help identify system scales. By considering a large number of optimizations, we quantify the variance of network diagnostics over optimizations ("optimization variance") and over randomizations of network structure ("randomization variance"). Because the modularity quality function typically has a large number of nearly degenerate local optima for networks constructed using real data, we develop a method to construct representative partitions that uses a null model to correct for statistical noise in sets of partitions. To illustrate our results, we employ ensembles of time-dependent networks extracted from both nonlinear oscillators and empirical neuroscience data. Many social, physical, technological, and biological systems can be modeled as networks composed of numerous interacting parts. 1 As an increasing amount of time-resolved data has become available, it has become increasingly important to develop methods to quantify and characterize dynamic properties of temporal networks. 2 Generalizing the study of static networks, which are typically represented using graphs, to temporal networks entails the consideration of nodes (representing entities) and/or edges (representing ties between entities) that vary in time. As one considers data with more complicated structures, the appropriate network analyses must become increasingly nuanced. In the present paper, we discuss methods for algorithmic detection of dense clusters of nodes (i.e., communities) by optimizing quality functions on multilayer network representations of temporal networks. 3,4 We emphasize the development and analysis of different types of null-model networks, whose appropriateness depends on the structure of the networks one is studying as well as the construction of representative partitions that take advantage of a multilayer network framework. To illustrate our ideas, we use ensembles of time-dependent networks from the human brain and human behavior.

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Section: Structural and Temporal Resolution Parametersmentioning

confidence: 99%

Robust detection of dynamic community structure in networks

Bassett

Porter

Wymbs

et al. 2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

484

645

View full text Add to dashboard Cite

show abstract

“…Nevertheless, they may have some disadvantages. For example, modularity-based algorithms may have resolution limit [16], which means they may be unable to find small communities without modifying their objective function [33]. In some cases, other algorithms can give high quality results when maximizing the modularity, but the time complexity could be high.…”

Section: Related Workmentioning

confidence: 99%

A scalable community detection algorithm for large graphs using stochastic block models

Peng

Zhang

Wong

et al. 2017

IDA

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“…The different curves provide a comparison between the exact calculation (thick line, Eqs. (6,7,28)), and independence approximation (thin solid line, Eq. (21)), and independence approximation with normal approximation (dotted line, Eq.…”

Section: An Independence Approximation For Community Edge Density mentioning

confidence: 99%

Algorithm independent bounds on community detection problems and associated transitions in stochastic block model graphs

et al. 2014

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We derive rigorous bounds for well-defined community structure in complex networks for a stochastic block model (SBM) benchmark. In particular, we analyze the effect of inter-community "noise" (inter-community edges) on any "community detection" algorithm's ability to correctly group nodes assigned to a planted partition, a problem which has been proven to be NP complete in a standard rendition. Our result does not rely on the use of any one particular algorithm nor on the analysis of the limitations of inference. Rather, we turn the problem on its head and work backwards to examine when, in the first place, well defined structure may exist in SBMs. The method that we introduce here could potentially be applied to other computational problems. The objective of community detection algorithms is to partition a given network into optimally disjoint subgraphs (or communities). Similar to k−SAT and other combinatorial optimization problems, "community detection" exhibits different phases. Networks that lie in the "unsolvable phase" lack well-defined structure and thus have no partition that is meaningful. Solvable systems splinter into two disparate phases: those in the "hard" phase and those in the "easy" phase. As befits its name, within the easy phase, a partition is easy to achieve by known algorithms. When a network lies in the hard phase, it still has an underlying structure yet finding a meaningful partition which can be checked in polynomial time requires an exhaustive computational effort that rapidly increases with the size of the graph. When taken together, (i) the rigorous results that we report here on when graphs have an underlying structure and (ii) recent results concerning the limits of rather general algorithms, suggest bounds on the hard phase.

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Narrow scope for resolution-limit-free community detection

Cited by 304 publications

References 33 publications

Robust detection of dynamic community structure in networks

Robust detection of dynamic community structure in networks

A scalable community detection algorithm for large graphs using stochastic block models

Algorithm independent bounds on community detection problems and associated transitions in stochastic block model graphs

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