Stochastic Pretopology as a Tool for Topological Analysis of Complex Systems

We are proposing in this paper a more general network modeling framework for complex system representation by introducing Stochastic Pretopology, a result of the combination of Pretopology theory and Random Sets. After giving the definition and some examples for building stochastic pretopology in many situations, we show how this approach generalizes graph, random graph, multi-relational networks and we present an application by giving Pretopology Cascade Model as a general model for information diffusion process that can take place in more complex networks such as multi-relational networks or stochastic graphs.