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We model the network using the Degree-Corrected Mixed-Membership (DCMM) model, where for each node $i$, there exists a membership vector $\\pi_i = (\\pi_i(1), \\pi_i(2), \\ldots, \\pi_i(K))'$, where $\\pi_i(k)$ is the weight that node $i$ puts in community $k$, $1 \\leq k \\leq K$. 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