Cycles and Components in Geometric Graphs: Adjacency Operator Approach
نویسندگان
چکیده
Nilpotent and idempotent adjacency operator methods are applied to the study of random geometric graphs in a discretized, d-dimensional unit cube [0, 1]. Cycles are enumerated, sizes of maximal connected components are computed, and closed formulas are obtained for graph circumference and girth. Expected numbers of k-cycles, expected sizes of maximal components, and expected circumference and girth are also computed by considering powers of adjacency operators.
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