Final Activity Report Summary - RANDIGRAPH (Random directed graph models with applications to epidemic processes and communication networks)
Many complex biological and physical systems such as epidemic processes and communication networks (e.g. the internet) can be studied by developing a random directed graph model of the system. To capture the essential features of such systems it may be necessary to construct models with certain additional properties or constraints. The main result of the research carried out under this fellowship has been to show how to construct a new, flexible random mapping model which can be used to model inhomogeneous systems where some vertices (i.e. nodes) are more 'popular' than others.
We have characterised the graphical structure of this new model under arbitrary assumptions about the underlying vertex 'popularity distribution' (i.e. vertex in-degree distribution), and applications of this model to the statistical modelling of epidemic processes have been developed. The component structure of random directed graphs, and graphs which are generated by them, under some structural restrictions or degree assumptions, which follow from applications in cluster analysis, cryptology and computer science have also been investigated.
We have characterised the graphical structure of this new model under arbitrary assumptions about the underlying vertex 'popularity distribution' (i.e. vertex in-degree distribution), and applications of this model to the statistical modelling of epidemic processes have been developed. The component structure of random directed graphs, and graphs which are generated by them, under some structural restrictions or degree assumptions, which follow from applications in cluster analysis, cryptology and computer science have also been investigated.