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Agents with aberrant behavior are commonplace in today’s networks. There are fake profiles in social media, malicious websites on the internet, and fake news sources that are prolific in spreading misinformation. The distinguishing characteristic of networks with aberrant agents is that normal agents rarely link to aberrant ones. Based on this manifested behavior, we propose a directed Markov Random Field (MRF) formulation for detecting aberrant agents. The formulation balances two objectives: to have as few links as possible from normal to aberrant agents, as well as to deviate minimally from prior information (if given). The MRF formulation is solved optimally and efficiently. We compare the optimal solution for the MRF formulation to existing algorithms, including PageRank, TrustRank, and AntiTrustRank. To assess the performance of these algorithms, we present a variant of the modularity clustering metric that overcomes the known shortcomings of modularity in directed graphs. We show that this new metric has desirable properties and prove that optimizing it is NP-hard. In an empirical experiment with twenty-three different datasets, we demonstrate that the MRF method outperforms the other detection algorithms.