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While networks have been the standard mathematical representation for detailedarrangements of relations in society, the simplicity of the representation limits whatinformation can be preserved in the abstraction, and subsequently, what can bemathematically analyzed. In this paper, we introduce a more rigorous and flexibleabstraction for representing arrangements of relations in society, the Messy Structure.After introducing the representational form and theoretically justifying it, we introducesome basic generative procedures for creating Messy Structures with “hierarchical”properties.