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Title: Understanding community structure for large networks
Author: Franke, B.
ISNI:       0000 0004 8498 523X
Awarding Body: UCL (University College London)
Current Institution: University College London (University of London)
Date of Award: 2016
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The general theme of this thesis is to improve our understanding of community structure for large networks. A scientific challenge across fields (e.g., neuroscience, genetics, and social science) is to understand what drives the interactions between nodes in a network. One of the fundamental concepts in this context is community structure: the tendency of nodes to connect based on similar characteristics. Network models where a single parameter per node governs the propensity of connection are popular in practice. They frequently arise as null models that indicate a lack of community structure, since they cannot readily describe networks whose aggregate links behave in a block-like manner. We generalize such a model called the degree-based model to a flexible, nonparametric class of network models, covering weighted, multi-edge, and power-law networks, and provide limit theorems that describe their asymptotic properties. We establish a theoretical foundation for modularity: a well-known measure for the strength of community structure and derive its asymptotic properties under the assumption of a lack of community structure (formalized by the class of degree-based models described above). This enables us to assess how informative covariates are for the network interactions. Modularity is intuitive and practically effective but until now has lacked a sound theoretical basis. We derive modularity from first principles, and give it a formal statistical interpretation. Moreover, by acknowledging that different community assignments may explain different aspects of a network's observed structure, we extend the applicability of modularity beyond its typical use to find a single "best" community assignment. We develop from our theoretical results a methodology to quantify network community structure. After validating it using several benchmark examples, we investigate a multi-edge network of corporate email interactions. Here, we demonstrate that our method can identify those covariates that are informative and therefore improves our understanding of the network.
Supervisor: Wolfe, P. J. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available