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The dissemination of information in clusters of social networks can be modeled as a probabilistic spreading process on complete graphs. This project analyzes various features of this model. We assume an individual in a cluster of a network starts a rumor (“infection”), and the rumor transmits to (“infects”) other connected individuals in each time step. We use Markov chains to analyze the model and find the probability distributions to describe the uncertain number of infected nodes after some time steps. Moreover, we characterize the Jordan form of the transition matrix of the Markov chain and analyze the expected time it takes the infection to spread to all nodes in the graph. Finally we consider a continuous-time version of the spreading process and the corresponding continuous-time Markov chain in which we determine the expected time until all nodes are infected.
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Jiang, Yushan, "The Analysis of Probabilistic Spread on Complete Graphs" (2014). Senior Projects Spring 2014. 302.
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