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This paper considers a Markov-modulated duplication-deletion random graphwhere at each time instant, one node can either join or leave the network; theprobabilities of joining or leaving evolve according to the realization of afinite state Markov chain. The paper comprises of 2 results. First, motivatedby social network applications, we analyze the asymptotic behavior of thedegree distribution of the Markov-modulated random graph. Using the asymptoticdegree distribution, an expression is obtained for the delay in searching suchgraphs. Second, a stochastic approximation algorithm is presented to trackempirical degree distribution as it evolves over time. The tracking performanceof the algorithm is analyzed in terms of mean square error and a functionalcentral limit theorem is presented for the asymptotic tracking error.

Tracking the Empirical Distribution of a Markov-modulated Duplication-Deletion Random Graph