We study the problem of identifying differentially mutated subnetworks of a large gene-gene interaction network, that is, subnetworks that display a significant difference in mutation frequency in two sets of cancer samples. We formally define the associated computational problem and show that the problem is NP-hard. We propose a novel and efficient algorithm, called DAMOKLE to identify differentially mutated subnetworks given genome-wide mutation data for two sets of cancer samples. We prove

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... at DAMOKLE identifies subnetworks with a statistically significant difference in mutation frequency when the data comes from a reasonable generative model, provided enough samples are available. We test DAMOKLE on simulated and real data, showing that DAMOKLE does indeed find subnetworks with significant differences in mutation frequency and that it provides novel insights not obtained by standard methods.