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A crystal net can be derived from a `generalized' voltage graph representing a graph analog of a fundamental domain of that crystal net along with a sufficient collection of its symmetries. The voltage assignments include not only isometries to the (oriented) edges, but also `weight' groups assigned to vertices for generating the vertex figures around those vertices. By varying the voltage assignments, one obtains geometrically distinct – and occasionally topologically distinct – Euclidean graphs. The focus here is on deriving simple graphs, i.e. graphs with no loops or lunes, especially uninodal edge transitive graphs.

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Portable Document Format (PDF) file https://doi.org/10.1107/S205327332300949X/vt5002sup1.pdf
Pseudocode for generating a unit cell of a simple graph


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