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We consider the problem of selecting important nodes in a random network,where the nodes connect to each other randomly with certain transitionprobabilities. The node importance is characterized by the stationaryprobabilities of the corresponding nodes in a Markov chain defined over thenetwork, as in Google's PageRank. Unlike deterministic network, the transitionprobabilities in random network are unknown but can be estimated by sampling.Under a Bayesian learning framework, we apply the first-order Taylor expansionand normal approximation to provide a computationally efficient posteriorapproximation of the stationary probabilities. In order to maximize theprobability of correct selection, we propose a dynamic sampling procedure whichuses not only posterior means and variances of certain interaction parametersbetween different nodes, but also the sensitivities of the stationaryprobabilities with respect to each interaction parameter. Numerical experimentresults demonstrate the superiority of the proposed sampling procedure.

Efficient Sampling for Selecting Important Nodes in Random Network