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Exponential Random Graph Modeling for Complex Brain Networks

By Sean L. Simpson, Satoru Hayasaka and Paul J. Laurienti

Abstract

Exponential random graph models (ERGMs), also known as p* models, have been utilized extensively in the social science literature to study complex networks and how their global structure depends on underlying structural components. However, the literature on their use in biological networks (especially brain networks) has remained sparse. Descriptive models based on a specific feature of the graph (clustering coefficient, degree distribution, etc.) have dominated connectivity research in neuroscience. Corresponding generative models have been developed to reproduce one of these features. However, the complexity inherent in whole-brain network data necessitates the development and use of tools that allow the systematic exploration of several features simultaneously and how they interact to form the global network architecture. ERGMs provide a statistically principled approach to the assessment of how a set of interacting local brain network features gives rise to the global structure. We illustrate the utility of ERGMs for modeling, analyzing, and simulating complex whole-brain networks with network data from normal subjects. We also provide a foundation for the selection of important local features through the implementation and assessment of three selection approaches: a traditional p-value based backward selection approach, an information criterion approach (AIC), and a graphical goodness of fit (GOF) approach. The graphical GOF approach serves as the best method given the scientific interest in being able to capture and reproduce the structure of fitted brain networks

Topics: Research Article
Publisher: Public Library of Science
OAI identifier: oai:pubmedcentral.nih.gov:3102079
Provided by: PubMed Central

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Citations

  1. (2009). A framework for the comparison of maximum pseudo-likelihood and maximum likelihood estimation of exponential family random graph models.
  2. (1974). A new look at the statistical model identification.
  3. (2010). A new measure of centrality for brain networks.
  4. (2009). Age- and gender related differences in the cortical anatomical network.
  5. (2009). Age-dependent features of EEGreactivity Spectral, complexity, and network characteristics.
  6. (2009). Age-related changes in modular organization of human brain functional networks.
  7. (2009). Aging and the interaction of sensory cortical function and structure.
  8. (2007). An introduction to exponential random graph (p*) models for social networks.
  9. (2002). Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain.
  10. (2009). Closure, connectivity and degree distributions: exponential random graph (p*) models for directed social networks.
  11. (1998). Collective dynamics of small-world networks.
  12. (2010). Comparison of characteristics between region- and voxel based network analysis in resting-state fMRI.
  13. (2009). Complex brain networks: graph theoretical analysis of structural and functional systems.
  14. (2010). Complex network measures of brain connectivity: uses and interpretations.
  15. (2010). Daffertshofer A
  16. (2010). Disrupted modularity and local connectivity of brain functional networks in childhood-onset schizophrenia.
  17. (2007). Exploring biological network structure using exponential random graph models.
  18. (2010). Functional Connectivity and brain networks in schizophrenia.
  19. (2008). Goodness of fit of social network models.
  20. (2007). Graph theoretical analysis of complex networks in the brain.
  21. (2009). Hierarchical modularity in human brain functional networks.
  22. (1999). Logit models and logistic regression for social networks: III. Valued relations.
  23. (1996). Logit models and logistic regressions for social networks: I.An introduction toMarkov graphsand p*.Psychometrika61:
  24. (1999). Logit models and logistic regressions for social networks: II. Multivariate relations.
  25. (2009). Mapping anatomical connectivity patterns of human cerebral cortex using in vivo diffusion tensor imaging tractography.
  26. (1986). Markov graphs.
  27. (2006). New specifications for exponential random graph models.
  28. (2009). On the geometry of discrete exponential families with application to exponential random graph models.
  29. (2007). Recent developments in exponential random graph (p*) models for social networks.
  30. (2002). Regression and ANOVA: an integrated approach using SAS software.
  31. (2008). Small-world and scale free organization of voxel-based resting-state functional connectivity in the human brain.
  32. (2006). Small-world brain networks.
  33. (2007). Small-world properties of nonlinear brain activity in schizophrenia.
  34. (2008). Specification of exponential-family random raph models: terms and computational aspects.
  35. (2002). Statistical models for social networks: Inference and degeneracy. Dynamic Social Network Modelling and Analysis: Workshop Summary
  36. (2008). statnet: Software tools for the statistical modeling of network data.
  37. (2008). Studying the human brain anatomical network via diffusionweighted MRI and graph theory.