Investigating the fine grained structure of networks

Abstract

In this thesis I explore a novel representation for characterizing a graph's fine grained structure. The key idea is that this structure can be represented as a distribution of the structural features of subgraphs. I introduce a set of such structural features and use them to compute representations for a variety of graphs, demonstrating their use in qualitatively describing fine structure. I then demonstrate the utility of this representation with quantitative techniques for computing graph similarity and graph clustering. I show that similarity judged using this representation is significantly different from judgements using full graph structural measures. I find that graphs from the same class of networks, such as email correspondence graphs, can differ significantly in their fine structure across the institutions whose relations they model, but also find examples of graphs from the same institutions across different time periods that share a similar fine structure.