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Modern graph or network datasets often contain rich structure that goesbeyond simple pairwise connections between nodes. This calls for complexrepresentations that can capture, for instance, edges of different types aswell as so-called "higher-order interactions" that involve more than two nodesat a time. However, we have fewer rigorous methods that can provide insightfrom such representations. Here, we develop a computational framework for theproblem of clustering hypergraphs with categorical edge labels --- or differentinteraction types --- where clusters corresponds to groups of nodes thatfrequently participate in the same type of interaction.  Our methodology is based on a combinatorial objective function that isrelated to correlation clustering on graphs but enables the design of much moreefficient algorithms that also seamlessly generalize to hypergraphs. When thereare only two label types, our objective can be optimized in polynomial time,using an algorithm based on minimum cuts. Minimizing our objective becomesNP-hard with more than two label types, but we develop fast approximationalgorithms based on linear programming relaxations that have theoreticalcluster quality guarantees. We demonstrate the efficacy of our algorithms andthe scope of the model through problems in edge-label community detection,clustering with temporal data, and exploratory data analysis.

Clustering in graphs and hypergraphs with categorical edge labels