Networks, communities, and consumer behaviour

Networks are an abstract representation of connections (the "edges") between entities (the "nodes"). One can represent many different types of data in this way, including many social, biological, technological and physical systems. Examples we discuss in this thesis include networks of friendship ties between individuals on Facebook, coauthorship networks between scientists, and similarities in voting patterns between members of the US Congress. Analysing intermediate-sized (or "meso-scale") features often reveals insights about a network's structure and function. A particular type of meso-scale feature are "communities", where one typically thinks of a community as a set of nodes that is particularly "well-connected" internally but has "few" connections to other nodes in a network. A complementary interpretation of a community is as a set of nodes that "trap" a diffusion-like dynamical process for a "long" time. Based on this dynamical interpretation, we investigate "size-resolved community structure" in networks by identifying bottlenecks of locally-biased dynamical processes that start at seed sets of nodes. By sampling many different local communities for different seeds and different strengths of the locality bias of the dynamical process, we obtain a picture of the way communities at different size scales compare in a network. This "size-resolved community structure" provides a signature of community structure in a network and its qualitative features are related to the way local communities combine to form the larger scale structure of a network. For many data sets, ordinary networks are not sufficient to represent the detailed connectivity patterns. For example, connections often evolve over time and one may have different types of connections between the same entities. Multilayer networks provide a framework to represent these different types of situations. The perspective of communities as bottlenecks to dynamical processes extends in a natural way to multilayer networks and we use it to illustrate that two types of random walk on a multilayer network that have been used as the basis for identifying communities in a multilayer network correspond to very different notions of what it means for a set of nodes to be a good multilayer community. This exemplifies the need for multilayer benchmark networks with known community structure to compare the ability of different methods to identify intuitive community structure. We propose a method for generating benchmark networks with general multilayer structure and use it as the basis for a preliminary comparison of different multilayer community detection methods. Finally, we use multilayer community detection to analyse survey data about people's perception of their hair. One key advantage of this type of data compared to most traditional network data sets is that we have a large number of potential explanatory variables that we can use to interpret the results of identifying communities which allows us to identify some potentially interesting hypothesis.