  In this paper, an iterative algorithm is designed to compute the sparse
graphs for traveling salesman problem (TSP) according to the frequency
quadrilaterals so that the computation time of the algorithms for TSP will be
lowered. At each computation cycle, the algorithm first computes the average
frequency \bar{f}(e) of an edge e with N frequency quadrilaterals containing e
in the input graph G(V,E). Then the 1/3|E| edges with low frequency are
eliminated to generate the output graph with a smaller number of edges. The
algorithm can be iterated several times and the original optimal Hamiltonian
cycle is preserved with a high probability. The experiments demonstrate the
algorithm computes the sparse graphs with the O(nlog_2n) edges containing the
original optimal Hamiltonian cycle for most of the TSP instances in the TSPLIB.
The computation time of the iterative algorithm is O(Nn^2).
