Stochastic Pretopology As A Tool For Complex Networks Analysis

We are proposing in this work a novel approach for complex network analysis by introducing Stochastic Pretopology, a result of the combination of Pretopology theory and Random Sets. We firstly show how pretopology generalizes the graph theory to deal with complex interactions in complex networks. By connecting with random set theory, we then give the definition of stochastic pretopology and also propose the ways to build this kind of pretopology in many situations. That is to say how proximity with randomness can be delivered to model complex neighbourhoods formation in complex networks. In addition, we also show how stochastic pretopology can be applied for modelling dynamic processes on complex networks by representing classical information diffusion models under stochastic pretopology language and then proposing 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.