{{1, 2}, {1, 4}, {1, 6}, {1, 10}, {1, 12}, {1, 16}, {1, 18},
{1, 22}, {1, 28}, {1, 30}, {2, 3}, {2, 5}, {2, 9}, {2, 11},
{2, 15}, {2,17}, {2, 21}, {2, 27}, {2, 29}, {3, 4}, {3, 8},
{3, 10}, {3,14}, {3, 16}, {3, 20}, {3, 26}, {3, 28}, {4, 7},
{4, 9}, {4,13}, {4, 15}, {4, 19}, {4, 25}, {4, 27}, {5, 6},
{5, 8}, {5,12}, {5, 14}, {5, 18}, {5, 24}, {5, 26}, {5, 32},
{6, 7}, {6,11}, {6, 13}, {6, 17}, {6, 23}, {6, 25}, {6, 31},
{7, 10}, {7,12}, {7, 16}, {7, 22}, {7, 24}, {7, 30}, {8, 9},
{8, 11}, {8,15}, {8, 21}, {8, 23}, {8, 29}, {9, 10}, {9, 14},
{9, 20}, {9,22}, {9, 28}, {9, 32}, {10, 13}, {10, 19}, {10, 21},
{10, 27}, {10,31}, {11, 12}, {11, 18}, {11, 20}, {11, 26}, {11, 30},
{11, 32}, {12, 17}, {12, 19}, {12, 25}, {12, 29}, {12, 31}, {13, 16},
{13, 18}, {13, 24}, {13, 28}, {13, 30}, {14, 15}, {14, 17}, {14, 23},
{14, 27}, {14, 29}, {15, 16}, {15, 22}, {15, 26}, {15, 28}, {15, 32},
{16, 21}, {16, 25}, {16, 27}, {16, 31}, {17, 20}, {17, 24}, {17, 26},
{17, 30}, {18, 19}, {18, 23}, {18, 25}, {18, 29}, {19, 22}, {19, 24},
{19, 28}, {20, 21}, {20, 23}, {20, 27}, {21, 22}, {21, 26}, {21, 32},
{22, 25}, {22, 31}, {23, 24}, {23, 30}, {24, 29}, {25, 28}, {26, 27},
{27, 32}, {28, 31}, {29, 30}, {29, 32}, {30, 31}}
I would like to create a graph using this data set to describe the edges. How can I create a graph in mathematica using this data set. I will need to find a hamiltonian path after I create the graph. if you have any ideas about finding the hamiltonian path then please include that in your answer.