| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 100 === In this thesis, we introduce a rumor spreading model based on the common susceptible-infected (SI) model which is a well known epidemiological model. We describe the maximum likelihood estimators of graphs and we evaluate the detection probabilities of finding the rumor source in d-regular trees. We observe that: For paths, the detection probability of finding the rumor source scales as t^(-1/2), which approaches 0 as t approaches infinity. For regular trees, we find an explicit bound of the detection probabilities of finding the source in d-regular trees. As a consequence, for d=3, the detection probability approaches 1/4, this result has been obtained earlier by using a random graph model.
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