Robust detection of dynamic community structure in networks
Open accessAbstract
We describe techniques for the robust detection of community structure in some classes of time-dependent 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.
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A common method for dealing with near degeneracy of the modularity quality function is to examine statistics averaged over 100 repetitions of the optimization, with equal weight placed on each solution rather than only on unique solutions.
“However, as of today, a common method for dealing with this degeneracy is to examine statistics averaged over the 100 repetitions of the optimization, with equal weight being placed on each solution, rather than just on the unique solutions.”
From Dynamic reconfiguration of frontal brain networks during executive cognition in humans (2015) · cites this paper as [25]
In a following methods paper (25), the authors stringently evaluated the methodological choices required to robustly detect dynamic community structure in simulated and empirical data.
“In a following methods paper (25), we stringently evaluated the methodological choices required to robustly detect dynamic community structure in simulated and empirical data.”
From Dynamic reconfiguration of frontal brain networks during executive cognition in humans (2015) · cites this paper as [25]
In that methods paper, simulated data from Kuramoto oscillators on known community structure demonstrated the ability of the computational techniques to successfully recover that structure.
“In that paper, we used simulated data from Kuramoto oscillators (for which there is a large literature illustrating their utility as “neural state” nodes; see, for example, ref. 58 and references therein) on known community structure and demonstrated the ability of the computational techniques to successfully recover that structure.”
From Dynamic reconfiguration of frontal brain networks during executive cognition in humans (2015) · cites this paper as [25]
In that methods paper, a framework of null model testing for statistical inference in neuroimaging data was developed.
“In that paper, we also developed a framework of null model testing for statistical inference in the context of neuroimaging data.”
From Dynamic reconfiguration of frontal brain networks during executive cognition in humans (2015) · cites this paper as [25]
Repeated optimizations of the modularity quality function of the consensus matrix Tcons return a single optimal consensus partition S, which partitions brain regions into representative putative functional modules that the authors interpret as cognitive systems.
“This procedure can be repeated iteratively, so that repeated optimizations of the modularity quality function of the consensus matrix Tcons return a single optimal consensus partition S, which partitions brain regions into representative putative functional modules that we interpret as cognitive systems (25).”
From Dynamic reconfiguration of frontal brain networks during executive cognition in humans (2015) · cites this paper as [25]
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Self-citation
- Authors
- Bassett, D. S., Porter, M. A., Wymbs, N. F., Grafton, S. T., Carlson, J. M., & Mucha, P. J.
- Affiliations
- University of California, Santa Barbara (US)
- University of Oxford (GB)
- University of North Carolina at Chapel Hill (US)
- ORCID
- Grafton, Scott T.
- Venue
- Chaos: An Interdisciplinary Journal of Nonlinear Science
- Publisher
- AIP Publishing
- Published
- 2013-03-01
- Volume
- 23
- Issue
- 1
- Pages
- 013142-013142
- ISSN
- 1054-1500 (ISSN-L)
- 1089-7682
- PMC
- PMC3618100
- OpenAlex
- W1983099884
- Cited by
- 425
- References
- 68
- Citations by year
- 2026: 16 · 2025: 30 · 2024: 30 · 2023: 23 · 2022: 35 · 2021: 36 · 2020: 40 · 2019: 34 · 2018: 43 · 2017: 49 · 2016: 38 · 2015: 24 · 2014: 21 · 2013: 6
- FWCI
- 20.92
- Type
- journal article
- Language
- en
- Open access
- green
- europepmc.org
- Locations
- Chaos An Interdisciplinary Journal of Nonlinear Science (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Engineering and Physical Sciences Research Council (EP/J001759/1)
- National Institute of General Medical Sciences (R21GM099493)
- National Institute of Neurological Disorders and Stroke (NS 44393, P01NS044393)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Physical Sciences › Computer Science › Computer Networks and Communications › Nonlinear Dynamics and Pattern Formation
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Complex Systems and Time Series Analysis
- Keywords
- community detection, time-dependent networks, null models, modularity, local optima, nonlinear oscillators
- MeSH terms
- Algorithms, Humans, Image Processing, Computer-Assisted, Magnetic Resonance Imaging, Models, Neurological, Motor Activity, Nerve Net, Oscillometry, Social Behavior, Systems Theory, Time Factors, Models, Statistical, Nonlinear Dynamics, Social Networking
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Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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