A Theoretical Study on Event Spreading Prediction by Probabilistic Connectivity Analysis in Dispersive Networks

This study discusses a potential use of probabilistic connectivity analysis for prediction of future progresses of events in stochastic network models. Probabilistic relation graphs provide a useful mathematical tool for representation of stochastic network models such as Markov chain models and random transitive networks. These stochastic network models have been widely and effectively used for analysis purpose in a range of application areas (e.g. statistics, language processing, genetics…). In this fashion, the current study investigates applications of the graph connectivity analysis based on taking powers of probabilistic relation matrices. Such probabilistic connectivity analysis can provide knowledge for prediction of future progress of spreading stochastic events in dispersive networks. Some properties of a stochastic dispersive network can be explored by taking power of probabilistic relation matrix, which indeed yields a probabilistic projection for future progress of the network in probability domain. Paper aims to develop a basic understanding for applications of probabilistic connectivity analysis for dispersive networks. Accordingly, applications of this analysis are considered, and illustrative examples are presented for discussion.