Understanding network concepts in modules
Open accessAbstract
BACKGROUND: Network concepts are increasingly used in biology and genetics. For example, the clustering coefficient has been used to understand network architecture; the connectivity (also known as degree) has been used to screen for cancer targets; and the topological overlap matrix has been used to define modules and to annotate genes. Dozens of potentially useful network concepts are known from graph theory. RESULTS: Here we study network concepts in special types of networks, which we refer to as approximately factorizable networks. In these networks, the pairwise connection strength (adjacency) between 2 network nodes can be factored into node specific contributions, named node 'conformity'. The node conformity turns out to be highly related to the connectivity. To provide a formalism for relating network concepts to each other, we define three types of network concepts: fundamental-, conformity-based-, and approximate conformity-based concepts. Fundamental concepts include the standard definitions of connectivity, density, centralization, heterogeneity, clustering coefficient, and topological overlap. The approximate conformity-based analogs of fundamental network concepts have several theoretical advantages. First, they allow one to derive simple relationships between seemingly disparate networks concepts. For example, we derive simple relationships between the clustering coefficient, the heterogeneity, the density, the centralization, and the topological overlap. The second advantage of approximate conformity-based network concepts is that they allow one to show that fundamental network concepts can be approximated by simple functions of the connectivity in module networks. CONCLUSION: Using protein-protein interaction, gene co-expression, and simulated data, we show that a) many networks comprised of module nodes are approximately factorizable and b) in these types of networks, simple relationships exist between seemingly disparate network concepts. Our results are implemented in freely available R software code, which can be downloaded from the following webpage: http://www.genetics.ucla.edu/labs/horvath/ModuleConformity/ModuleNetworks.
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Hierarchical clustering on the network structure allows uncovering functional modules of genes whose expression profiles are tightly intertwined, which typically correspond to specific biological processes and disease states.
“Hierarchical clustering on the network structure allows us to uncover functional modules of genes whose expression profiles are tightly intertwined,3,4 which typically correspond to specific biological processes and disease states.”
From hdWGCNA identifies co-expression networks in high-dimensional transcriptomics data (2023) · cites this paper as [4]
The Background section describes defining modules as branches of a hierarchical-clustering dendrogram, and the Results section applies this method to gene co-expression networks. The Results also report that most modules are enriched for known gene ontologies, supporting a link to biological functions. The paper does not establish that these modules typically correspond to disease states. (LLM, conf=0.87)
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- Authors
- Dong, J., & Horvath, S.
- Affiliations
- University of California, Los Angeles (US)
- Corresponding author
- Horvath, Steve
- Venue
- BMC Systems Biology
- Published
- 2007-06-04
- Volume
- 1
- Issue
- 1
- Pages
- 24-24
- ISSN
- 1752-0509 (ISSN-L)
- PMC
- PMC3238286
- OpenAlex
- W2057498577
- Cited by
- 455
- References
- 54
- Citations by year
- 2026: 2 · 2025: 22 · 2024: 14 · 2023: 19 · 2022: 29 · 2021: 37 · 2020: 26 · 2019: 28 · 2018: 23 · 2017: 33 · 2016: 18 · 2015: 33 · 2014: 34 · 2013: 38 · 2012: 30
- FWCI
- 5.57
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- BMC Systems Biology (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Funders
- National Institutes of Health (1u24ns043562-01)
- National Institute of Mental Health
- National Institute of Allergy and Infectious Diseases (U19AI063603)
- National Institute of Neurological Disorders and Stroke (1U24NS043562-01)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Bioinformatics and Genomic Networks
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Physical Sciences › Mathematics › Geometry and Topology › Graph theory and applications
- Keywords
- network concept, module networks, connectivity, clustering coefficient, network heterogeneity, network density, centralization, gene co-expression network, protein-protein interaction network, network module detection
- MeSH terms
- Animals, Computer Simulation, Drosophila, Models, Biological, Terminology as Topic, Proteins, Yeasts, Gene Expression, Cluster Analysis, Gene Regulatory Networks, Metabolic Networks and Pathways
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