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Cayley Graphs — Group Structure as Geometry

Every group becomes a graph when you connect elements by generators — symmetry becomes topology

Nodes = group elements. Edges = right-multiplication by generator (colored by generator). Abelian groups have commutative diagrams; non-abelian groups (S₃, D₄, Q₈) show asymmetric edge patterns. Colors show element order, coset membership, or index. Drag nodes to rearrange.