  Geometrically frustrated assemblies where building blocks misfit have been
shown to generate intriguing phenomena from self-limited growth, fiber
formation, to structural complexity. We introduce a graph theory formulation of
geometrically frustrated assemblies, capturing frustrated interactions through
the concept of incompatible flows, providing a direct link between structural
connectivity and frustration. This theory offers a minimal yet comprehensive
framework for the fundamental statistical mechanics of frustrated assemblies.
Through numerical simulations, the theory reveals new characteristics of
frustrated assemblies, including two distinct percolation transitions for
structure and stress, a crossover between cumulative and non-cumulative
frustration controlled by disorder, and a divergent length scale in their
response.
