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Probabilistic Analysis of Graphlets in Sparse E-R Random Graphs

Frequency counting of graphlets (i.e. small connected induced subgraphs) is a prominent experimental approach to network analysis which became favorable in bioinformatics. In this paper, we use the probabilistic method for graphlets counting. We show that it is possible to enumerate the graphlets (or isolated graphlets) in sparse Erdős-Rényi graph model analytically. Obtained frequencies are exploited to estimate bounds on domination number in the above mentioned random graph model.