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This paper unifies the theory of consistent-set maximization for robust outlier detection in a simultaneous localization and mapping framework. We first describe the notion of pairwise consistency before discussing how a consistency graph can be formed by evaluating pairs of measurements for consistency. Finding the largest set of consistent measurements is transformed into an instance of the maximum clique problem and can be solved relatively quickly using existing maximum-clique solvers. We then generalize our algorithm to check consistency on a group- k basis by using a generalized notion of consistency and using generalized graphs. We also present modified maximum clique algorithms that function over generalized graphs to find the set of measurements that is internally group- k consistent. We address the exponential nature of group- k consistency and present methods that can substantially decrease the number of necessary checks performed when evaluating consistency. We extend our prior work to perform data association, and to multi-agent systems in both simulation and hardware, and provide a comparison with other state-of-the-art methods.