Given a connected crystalline structure, the set of paths and cycles of the quotient graph of its bond net is embedded into a commutative ring structure. Multiplication combines walks to build up geodesics of the net whereas addition stands symbolically for enumerating a collection of walks. Topological criteria are used to define zero divisors which enable the development of an algebraic generator into a combination of geodesics that are in a one-to-one correspondence with the vertices of the net. A ring mapping gives the generating function of the coordination sequence in the net.
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