Abstract: One method for counting weighted cycle systems in a graph entails taking the determinant of the identity matrix minus the adjacency matrix of the graph. The result of this operation is the sum over cycle systems of -1 to the power of the number of disjoint cycles times the weight of the cycle system. The author uses this fact to reprove that the determinant of a matrix of much smaller order can be computed to calculate the number of cycle systems in a hamburger graph.

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