Structure and dynamics of social bipartite and projected networks

Abstract

Networks have become ubiquitous across many areas of knowledge. Their popularity comes from the fact that, apart from the variety of the nature of the systems, they present similar architecture governed by universal properties. Moreover, networks function as a skeleton, by mapping the interactions between the elements of the system translated into nodes and links. We can use networks to represent even more complicated systems, e.g. those with elements of two different types. For such cases, we use bipartite networks. Despite their importance for the analysis of complex systems, bipartite networks are often neglected. In general, one-mode versions of the bipartite network are created using the preferred node type. However, such versions— one-mode projected networks — inherently present a loss of information, which would most likely result in impaired analysis. The goal of this thesis is to provide further knowledge about the structure of bipartite networks and, more importantly, how it affects the structural properties of projected networks. First, we show the causality between the degree distributions of bipartite networks and the resulting degree distribution of projected networks. Also, we find that the bipartite degree distributions are not the only feature driving topology formation in projected networks. Thus, we move forward to another network structural feature: small cycles. They represent types of clustering in bipartite networks and directly affect the projected network structure. We use empirical and synthetic networks to show that while four-cycles indicate recurrence of links between a pair of nodes in the projections, six-cycles — representation of transitivity— affect clustering levels. Third, we introduce the dynamics of network growth. We use extensive datasets to study the evolution of the structure of scientific collaboration networks. We create a comprehensive mapping of how several network structural properties evolve over time. Finally, we propose a generative model for bipartite networks. It is a bipartite extension of a model previously designed for one-mode networks. We show that with the proper adaptation, the model can assess the fundamental structural properties that we have studied throughout the thesis, reproducing both bipartite and projected network features.