Interaction Topologies and Information Flow

Networks are ubiquitous, underlying systems as diverse as the Internet, food webs, societal interactions, the cell, and the brain. Of crucial importance is the coupling of network structure with system dynamics, and much recent attention has focused on how information, such as pathogens, mutations, or ideas, ow through networks. In this dissertation, we advance the understanding of how network structure a ects information ow in two important classes of models. The rst is an independent interaction model, which is used to investigate the propagation of advantageous alleles in evolutionary algorithms. The second is a threshold model, which is used to study the dissemination of ideas, fads, and innovations throughout populations. This journal-format dissertation comprises three interrelated studies, in which we investigate the in uence of network structure on the dynamical properties of information ow. In the rst study, we develop an analytical technique to approximate system dynamics in arbitrarily structured regular interaction topologies. In the second study, we investigate the ow of advantageous alleles in degree-correlated scale-free population structures, and provide a simple topological metric for assessing the selective pressures induced by these networks. In the third study, we characterize the conditions in which global information cascades occur in threshold models of binary decisions with externalities, structured on degree-correlated Poisson-distributed random networks.