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Cited by 1,161Functional Brain Connectivity StudiesComplex Network Analysis TechniquesAdvanced Neuroimaging Techniques and Applications

Comparing Brain Networks of Different Size and Connectivity Density Using Graph Theory

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van Wijk, Bernadette C. M., Stam, Cornelis J., Daffertshofer, Andreas·2010·PLoS ONE
DOI 10.1371/journal.pone.0013701PMC PMC2965659
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Abstract

Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N) and the average degree (k) of the network. The explicit form of that influence depends on the type of network topology, which is usually unknown for experimental data. Direct comparisons of graph measures between empirical networks with different N and/or k can therefore yield spurious results. We list benefits and pitfalls of various approaches that intend to overcome these difficulties. We discuss the initial graph definition of unweighted graphs via fixed thresholds, average degrees or edge densities, and the use of weighted graphs. For instance, choosing a threshold to fix N and k does eliminate size and density effects but may lead to modifications of the network by enforcing (ignoring) non-significant (significant) connections. Opposed to fixing N and k, graph measures are often normalized via random surrogates but, in fact, this may even increase the sensitivity to differences in N and k for the commonly used clustering coefficient and small-world index. To avoid such a bias we tried to estimate the N,k-dependence for empirical networks, which can serve to correct for size effects, if successful. We also add a number of methods used in social sciences that build on statistics of local network structures including exponential random graph models and motif counting. We show that none of the here-investigated methods allows for a reliable and fully unbiased comparison, but some perform better than others.

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  • Thresholding connectomes is necessary for removing false-positive edges and facilitating between-group comparisons but can remove potentially valid information regarding differences in network topology.

    “Thresholding connectomes is necessary for removing false-positive edges and facilitating between-group comparisons but can remove potentially valid information regarding differences in network topology (Fornito, Zalesky, & Breakspear, 2013; van Wijk, Stam, & Daffertshofer, 2010).”

    From Functional and structural connectome properties in the 5XFAD transgenic mouse model of Alzheimer’s disease (2018) · cites this paper as van Wijk, Stam, & Daffertshofer, 2010

    In Analysis > Defining graphs from data, the paper describes thresholding to omit connectivity values expected by chance and warns that a fixed average degree can exclude important connections and modify topology. It also says thresholding can hide information that differs between conditions. The claim overstates its necessity for between-group comparisons: the paper says threshold choice can make comparisons inaccurate and discusses weighted analysis as an alternative that avoids selecting a threshold. (LLM, conf=0.86)

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Cited by

Sorted by citations

Authors
van Wijk, B. C. M., Stam, C. J., & Daffertshofer, A.
Affiliations
  • Amsterdam UMC Location Vrije Universiteit Amsterdam (NL)
  • Vrije Universiteit Amsterdam (NL)
ORCID
Venue
PLoS ONE
Publisher
Public Library of Science (PLoS)
Published
2010-10-28
Volume
5
Issue
10
Pages
e13701
ISSN
1932-6203 (ISSN-L)
DOI
10.1371/journal.pone.0013701
PMC
PMC2965659
OpenAlex
W2166148649
Cited by
1,161
References
7
Citations by year
2026: 58 · 2025: 58 · 2024: 65 · 2023: 72 · 2022: 72 · 2021: 94 · 2020: 90 · 2019: 118 · 2018: 98 · 2017: 86 · 2016: 86 · 2015: 74 · 2014: 72 · 2013: 53 · 2012: 46
FWCI
22.50
Type
journal article
Language
en
Open access
Licence
Locations
  • PLoS ONE (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • Pure Amsterdam UMC (publishedVersion, other-oa)
  • Amsterdam UMC (VU Amsterdam) - Institutional Repository (publishedVersion, other-oa)
  • VU Research Portal (publishedVersion, other-oa)
  • Data Archiving and Networked Services (DANS) (submittedVersion, other-oa)
  • RePEc: Research Papers in Economics (submittedVersion)
  • Digital Academic REpository of VU University Amsterdam (Vrije Universiteit Amsterdam) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • UCL Discovery (University College London) (submittedVersion)
  • Figshare (submittedVersion, cc-by)
Funders
Nederlandse Organisatie voor Wetenschappelijk Onderzoek
Topics
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
  • Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced Neuroimaging Techniques and Applications
Keywords
brain network topology, network size effects, connectivity density, clustering coefficient, weighted graphs, exponential random graph models, motif counting
MeSH terms
Brain, Humans

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