Morpho-Statistical Description of Networks Through Graph Modelling and Bayesian Inference

Collaboration graphs are relevant sources of information to understand behavioural tendencies of groups of individuals. The study of these graphs enables figuring out factors that may affect the efficiency and the sustainability of cooperative work. For example, such a collaboration involves researchers who develop relationships with their external counterparts to address scientific challenges. As relations and projects change over time, the evolution of social structures must be tackled. We propose a statistical approach considering different structural collaboration patterns and captures the dynamic of the relational structures over the years. Our approach combines spatial processes modelling and Exponential Random Graph Models used to analyse social processes. Since the normalising constant involved in classical Markov Chain Monte Carlo (MCMC) approaches is intractable, the inference remains challenging. To overcome this issue, we propose a Bayesian tool that relies on the recent ABC Shadow algorithm. The method is illustrated on real data sets from an open archive of scholarly documents. Through a simple formalism, our approach highlights the interactions between the different types of social relations at stake in the collaboration network.