Degree distributions, correlations, and information spread on networks

In this thesis we study several topics within the field of network science. This work can largely be divided into studies of network structure and dynamics on networks. First, we study the structure of networks and network algorithms, focused primarily on the degree distributions of networks and the presence of correlations among the degrees of network nodes.In particular, we describe a method for fitting degree distributions. We develop a new degree-preserving rewiring algorithm which outperforms current methods. To unite these two pieces of work, we put our rewiring algorithm to use in investigating the long-range correlations in that exist between properties of network nodes, and explore how these correlations relate to degree distributions.Following this, we turn our attention to information diffusion on networks with an innovative model of meme spread, which allows for the accounting of varying meme quality. We show detailed results in terms of how memes spread in the presence of other memes of different levels of fitness, with remarkable qualities for a model of self-organised criticality.