Many complex systems can be represented as graphs or networks. In numerous applications it is not possible or desirable to observe the entire network structure.
We might instead be able to infer a parametric model of the network. In the case of social networks, we might have access to the demographic coordinates of individuals
(e.g. age, income) and the corresponding propensities for individuals of different demographics to share ties. In this thesis I investigate the extent to which we
predict properties of and influence dynamical processes occurring on graphs given only some parametric model of the network.
The first part of this thesis explores the properties of ensembles of Random Geometric Graphs (RGGs), which are simple models of homophilous social networks. The
algebraic connectivity is a graph property which is inversely related to the timescale
of linear diffusion. I use numerical simulations to provide the first characterisation of the algebraic connectivity distribution in RGGs. I show for some ensembles, involving larger numbers of nodes, that this distribution exhibits appreciable fluctuations. My results demonstrate that it is not generally possible to predict the properties of RGGs by knowing only the ensemble – more detailed knowledge of the node positions for a specific graph is typically required. The second part of this thesis explores the extent to which we can influence large scale social systems given only knowledge of an individual’s demographics and their propensities to connect. We consider the problem of influencing Ising systems on partially observed graphs. We consider the Ising influence problem on synthetic
networks generated from stochastic block models and case studies of real world social
networks. We demonstrate how simple models which rely only on a coarse grained description of the system can perform comparably to more expensive optimisation algorithms that require complete knowledge of the graph.