Implications of clustering (motif-structure) for network-based processes

Networks are an incredibly powerful way of thinking about (and modelling) the interaction of individuals or particles. Probably the most familiar form of network is the social contacts that we form with friends, family and colleagues. These social networks are typical of the types of network we wish to understand: there are relatively few links (people only have a limited number of contacts compared to the total population), there is variability (some people have many more contacts than others), and the contacts are clustered (my contacts are likely to know each other). It is this final property of clustering that we wish to study in this grant proposal, and will focus on the spread of infectious diseases through clustered networks as our main example.Given the power of modern computers it is quick and easy to simulate the behaviour of any process (eg the spread of infection) on any network, and these simulations have shown that clustering within the network has a strong effect. However, this approach has two disadvantages. The first is that to simulate the behaviour we need to know the precise network, and unfortunately the collection of network data (especially for humans) is difficult and time-consuming - for this reason very few examples of true networks exist. The second problem is that simulation results only tell us about the particular network we are using, we do not know if our results are general or specific to our chosen network. For these reasons we want to used more abstract approaches that allow us to extract general results.One approach to achieve this is the use of pair-wise approximations - which model the number (and type) of interacting pairs, but ignore other elements of network structure. While such pair-wise models have been incredibly useful in understanding the behaviour of processes on a range of complex network types, there are several fundamental flaws when trying to use these approximations for clustered models. This proposal aims to overcome these flaws and therefore predict the general impact of clustering upon network processes. This has great importance for many subject areas where networks are considered important, including computer science, systems biology, genetics, sociology, epidemiology and complexity theory. Our new theoretical developments will be applied primarily to problems of infectious disease spread and control through human social networks. Improvements in this area will directly influence the models that are used to support public-health policies in the UK and elsewhere. However, there are a vast number of other subject areas that will directly benefit from the methods we develop. These include: genetics, computer science, social science and biology. We therefore feel that our work is likely to have far-reaching benefits for scientific researchers, which in turn will benefit the general public.