Network modeling and graph theory have been widely studied and applied in a variety of modern research areas. The detection of network structures in these contexts is a fundamental and challenging problem. "Community structures'' (where nodes are clustered into densely connected subnetworks) appear in a wide spectrum of disciplines. Examples include groups of individuals sharing common interests in social networks and groups of proteins carrying out similar biological functions. Detecting network structure also enables us to perform other kinds of network analysis, such as hub identification.
Modularity-based graph partitioning is an approach that is specifically designed to detect the community structures in a network. Though modularity methods have achieved some amount of success in detecting modular structures, many of the related problems have not yet been solved.
Central to modularity-based graph partitioning is the null model: a statistical representation of a network with no structure. In this work, I will present a novel approach to design null models. This new null model approach resolves many of the existing problems, including dealing with non-negativity, topological consistency, etc. Null models are presented for binary/weighted graphs and undirected/directed graphs. I will also present several new methods to assess the statistical significance of the detected community structures. Several of the potential future work directions as well as the position of the modular detection problem in a broader network analysis scheme will be given at the end of this thesis.
|Advisor:||Leahy, Richard M.|
|Commitee:||Kuo, C.-C. Jay, Tjan, Bosco|
|School:||University of Southern California|
|School Location:||United States -- California|
|Source:||DAI-B 73/11(E), Dissertation Abstracts International|
|Subjects:||Neurosciences, Electrical engineering|
|Keywords:||Brain connectome, Graph theory, Modularity, Network structures, Random matrix theory, Statistical significance|
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