Hidden features and information diffusion in large social networks

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In social networks, connections are made based on a degree of communality between the users. Typically, links are more likely if users share common features or belong to the same community. Network formation can be modelled by assuming the nodes to be embedded in a feature space, and links to be formed through a stochastic process which depends on the distance between the nodes in the underlying space. The aim of the proposed research is to develop models and algorithms that will allow for the extraction of the latent feature space from the link structure of large networks. I will use theoretical tools to study the relationship between spatial features of the nodes and the link structure, using the infinite limit to understand the behaviour as the network gets large. I will also further develop and analyze a spatial model for growing networks, built on the principle of preferential attachment, which leads to graphs that exhibit commonly observed features such as a power law degree distribution, high clustering, and the presence of long links that lead to the small world property.