Matrix Witnesses system:sage {{{id=82| import networkx.generators.atlas atlas_graphs = [Graph(i) for i in networkx.generators.atlas.graph_atlas_g()] /// }}} {{{id=75| def check_witness(Matrix,Number): print "Rank is ", Matrix.rank() print "Symmetric?", Matrix.is_symmetric() print "Isomorphic to graph G",Number," ",Graph(Matrix).is_isomorphic(atlas_graphs[Number]) print Matrix show(Graph(Matrix)) /// }}} {{{id=92| G721=Matrix([[-1, 1, 0, 0, 1,0,1],[1,-1,1,0,0,1,0],[0,1,-1,1,0,-1,0],[0,0,1,0,1,1,1], [1,0,0,1,0,0,0],[0,1,-1,1,0,-1,0],[1,0,0,1,0,0,0]]) check_witness(G721,721) /// Rank is 3 Symmetric? True Isomorphic to graph G 721 True [-1 1 0 0 1 0 1] [ 1 -1 1 0 0 1 0] [ 0 1 -1 1 0 -1 0] [ 0 0 1 0 1 1 1] [ 1 0 0 1 0 0 0] [ 0 1 -1 1 0 -1 0] [ 1 0 0 1 0 0 0] }}} {{{id=39| G801=Matrix([[0, 1, 1, 0, -1, -1, -1],[1, 1, 1, 1, 0, 0, 0],[1, 1, 1, 1, 0, 0, 0],[0, 1, 1, 0, -1, -1, -1], [-1, 0, 0, -1, 0, 0, 0],[-1, 0, 0,-1, 0, 0, 0],[-1, 0, 0,-1, 0, 0, 0]]) check_witness(G801,801) /// Rank is 3 Symmetric? True Isomorphic to graph G 801 True [ 0 1 1 0 -1 -1 -1] [ 1 1 1 1 0 0 0] [ 1 1 1 1 0 0 0] [ 0 1 1 0 -1 -1 -1] [-1 0 0 -1 0 0 0] [-1 0 0 -1 0 0 0] [-1 0 0 -1 0 0 0] }}} {{{id=17| G812=Matrix([[0,1,1,0,0,0,0],[1,0,0,1,1,0,1],[1,0,0,1,1,0,1],[0,1,1,1,1,1,0], [0,1,1,1,1,1,0],[0,0,0,1,1,1,0],[0,1,1,0,0,0,0]]) check_witness(G812,812) /// Rank is 3 Symmetric? True Isomorphic to graph G 812 True [0 1 1 0 0 0 0] [1 0 0 1 1 0 1] [1 0 0 1 1 0 1] [0 1 1 1 1 1 0] [0 1 1 1 1 1 0] [0 0 0 1 1 1 0] [0 1 1 0 0 0 0] }}} {{{id=18| G831=Matrix([[0,-1,1,0,0,0,0],[-1,0,1,0,0,1,-1],[1,1,-1,1,1,0,1], [0,0,1,1,1,1,0],[0,0,1,1,1,1,0],[0,1,0,1,1,1,0],[0,-1,1,0,0,0,0]]) check_witness(G831,831) /// Rank is 3 Symmetric? True Isomorphic to graph G 831 True [ 0 -1 1 0 0 0 0] [-1 0 1 0 0 1 -1] [ 1 1 -1 1 1 0 1] [ 0 0 1 1 1 1 0] [ 0 0 1 1 1 1 0] [ 0 1 0 1 1 1 0] [ 0 -1 1 0 0 0 0] }}} {{{id=19| G832=Matrix([[-1,-1,-1,0,0,0,-1],[-1,0,-2,-1,0,-1,-1],[-1,-2,-1,0,-1,0,-1],[0,- 1,0,0,-1,0,0],[0,0,-1,-1,-1,-1,0],[0,-1,0,0,-1,0,0],[-1,-1,-1,0,0,0,-1]]) check_witness(G832,832) /// Rank is 3 Symmetric? True Isomorphic to graph G 832 True [-1 -1 -1 0 0 0 -1] [-1 0 -2 -1 0 -1 -1] [-1 -2 -1 0 -1 0 -1] [ 0 -1 0 0 -1 0 0] [ 0 0 -1 -1 -1 -1 0] [ 0 -1 0 0 -1 0 0] [-1 -1 -1 0 0 0 -1] }}} {{{id=53| G846=matrix([[0, -2, 0, 0, 1, 0, 0], [-2, 0, 1, 0, 0, 1, 1], [0, 1,1/2, 1, 0, 1, 0], [0, 0, 1, 2, 1, 2, 0], [1, 0, 0, 1, 1/2,1/2, -1/2], [0, 1, 1, 2, 1/2, 2, 0], [0, 1, 0, 0, -1/2, 0, 0]]) check_witness(G846,846) /// Rank is 3 Symmetric? True Isomorphic to graph G 846 True [ 0 -2 0 0 1 0 0] [ -2 0 1 0 0 1 1] [ 0 1 1/2 1 0 1 0] [ 0 0 1 2 1 2 0] [ 1 0 0 1 1/2 1/2 -1/2] [ 0 1 1 2 1/2 2 0] [ 0 1 0 0 -1/2 0 0] }}} {{{id=20| G863=Matrix([[-1,1,1,0,0,0,-1],[1,-1,0,1,0,1,1],[1,0,0,1,1,0,1], [0,1,1,1,1,0,0],[0,0,1,1,0,1,0],[0,1,0,0,1,-1,0],[-1,1,1,0,0,0,-1]]) check_witness(G863,863) /// Rank is 3 Symmetric? True Isomorphic to graph G 863 True [-1 1 1 0 0 0 -1] [ 1 -1 0 1 0 1 1] [ 1 0 0 1 1 0 1] [ 0 1 1 1 1 0 0] [ 0 0 1 1 0 1 0] [ 0 1 0 0 1 -1 0] [-1 1 1 0 0 0 -1] }}} {{{id=21| G873=Matrix([[1,-1,-1,0,0,0,1],[-1,0,0,-1,0,-1,-1],[-1,0,0,-1,0,-1,-1],[0,-1,- 1,0,-1,0,0],[0,0,0,-1,1,-1,0],[0,-1,-1,0,-1,0,0],[1,-1,-1,0,0,0,1]]) check_witness(G873,873) /// Rank is 3 Symmetric? True Isomorphic to graph G 873 True [ 1 -1 -1 0 0 0 1] [-1 0 0 -1 0 -1 -1] [-1 0 0 -1 0 -1 -1] [ 0 -1 -1 0 -1 0 0] [ 0 0 0 -1 1 -1 0] [ 0 -1 -1 0 -1 0 0] [ 1 -1 -1 0 0 0 1] }}} {{{id=95| G878=Matrix([[-1, 1, 0, 0, 1,0,-1],[1,-1,1,0,0,1,1],[0,1,-1,1,0,-1,0],[0,0,1,0,1,1,0], [1,0,0,1,0,0,1],[0,1,-1,1,0,-1,0],[-1, 1, 0, 0, 1,0,-1]]) check_witness(G878,878) /// Rank is 3 Symmetric? True Isomorphic to graph G 878 True [-1 1 0 0 1 0 -1] [ 1 -1 1 0 0 1 1] [ 0 1 -1 1 0 -1 0] [ 0 0 1 0 1 1 0] [ 1 0 0 1 0 0 1] [ 0 1 -1 1 0 -1 0] [-1 1 0 0 1 0 -1] }}} {{{id=64| G913=Matrix([[1,1,1,1,0,0,0],[1,1,1,1,0,0,0],[1,1,2,2,1,1,1],[1,1,2,2,1,1,1],[0,0,1,1,0,0,0],[0,0,1,1,0,0,0],[0,0,1,1,0,0,0]]) check_witness(G913,913) /// Rank is 3 Symmetric? True Isomorphic to graph G 913 True [1 1 1 1 0 0 0] [1 1 1 1 0 0 0] [1 1 2 2 1 1 1] [1 1 2 2 1 1 1] [0 0 1 1 0 0 0] [0 0 1 1 0 0 0] [0 0 1 1 0 0 0] }}} {{{id=9| G918=Matrix([[0,-1,-1,0,0,0,0],[-1,-1,-1,-1,-1,0,-1],[-1,-1,-1,-1,-1,0,-1],[0,-1,-1,-1,-1,1,0],[0,-1,-1,-1,-1,1,0],[0,0,0,1,1,-1,0],[0,-1,-1,0,0,0,0]]) check_witness(G918,918) /// Rank is 3 Symmetric? True Isomorphic to graph G 918 True [ 0 -1 -1 0 0 0 0] [-1 -1 -1 -1 -1 0 -1] [-1 -1 -1 -1 -1 0 -1] [ 0 -1 -1 -1 -1 1 0] [ 0 -1 -1 -1 -1 1 0] [ 0 0 0 1 1 -1 0] [ 0 -1 -1 0 0 0 0] }}} {{{id=68| G924=Matrix([[0,0,1,1,0,0,0],[0,0,1,1,0,0,0],[1,1,1,1,1,0,0],[1,1,1,2,2,1,1], [0,0,1,2,1,1,1],[0,0,0,1,1,1,1],[0,0,0,1,1,1,1]]) check_witness(G924,924) /// Rank is 3 Symmetric? True Isomorphic to graph G 924 True [0 0 1 1 0 0 0] [0 0 1 1 0 0 0] [1 1 1 1 1 0 0] [1 1 1 2 2 1 1] [0 0 1 2 1 1 1] [0 0 0 1 1 1 1] [0 0 0 1 1 1 1] }}} {{{id=10| G932=Matrix([[0,-1,-1,0,0,0,0],[-1,-2,-1,2,-1,0,-1],[-1,-1,-1,1,0,-1,-1], [0,2,1,-1,1,-1,0],[0,-1,0,1,-1,1,0],[0,0,-1,-1,1,-1,0],[0,-1,-1,0,0,0,0]]) check_witness(G932,932) /// Rank is 3 Symmetric? True Isomorphic to graph G 932 True [ 0 -1 -1 0 0 0 0] [-1 -2 -1 2 -1 0 -1] [-1 -1 -1 1 0 -1 -1] [ 0 2 1 -1 1 -1 0] [ 0 -1 0 1 -1 1 0] [ 0 0 -1 -1 1 -1 0] [ 0 -1 -1 0 0 0 0] }}} {{{id=23| G944=Matrix([[1,1,1,0,0,0,1],[1,1,2,0,1,1,2],[1,2,1,1,0,0,1],[0,0,1,0,1,1,1], [0,1,0,1,0,0,0],[0,1,0,1,0,0,0],[1,2,1,1,0,0,1]]) check_witness(G944,944) /// Rank is 3 Symmetric? True Isomorphic to graph G 944 True [1 1 1 0 0 0 1] [1 1 2 0 1 1 2] [1 2 1 1 0 0 1] [0 0 1 0 1 1 1] [0 1 0 1 0 0 0] [0 1 0 1 0 0 0] [1 2 1 1 0 0 1] }}} {{{id=78| G953=Matrix([[-2,1,0,1,0,0,0],[1,0,1/2,0,1,1/2,1/2], [0,1/2,1,1,1,0,0],[1,0,1,1/2,1,0,0], [0,1,1,1,2,1,1],[0,1/2,0,0,1,1,1],[0,1/2,0,0,1,1,1]]) check_witness(G953,953) /// Rank is 3 Symmetric? True Isomorphic to graph G 953 True [ -2 1 0 1 0 0 0] [ 1 0 1/2 0 1 1/2 1/2] [ 0 1/2 1 1 1 0 0] [ 1 0 1 1/2 1 0 0] [ 0 1 1 1 2 1 1] [ 0 1/2 0 0 1 1 1] [ 0 1/2 0 0 1 1 1] }}} {{{id=25| G956=Matrix([[1,1,0,1,1,1,1],[1,0,1,0,0,1,0],[0,1,0,1,0,0,0],[1,0,1,0,0,1,0], [1,0,0,0,1,1,1],[1,1,0,1,1,1,1],[1,0,0,0,1,1,1]]) check_witness(G956,956) /// Rank is 3 Symmetric? True Isomorphic to graph G 956 True [1 1 0 1 1 1 1] [1 0 1 0 0 1 0] [0 1 0 1 0 0 0] [1 0 1 0 0 1 0] [1 0 0 0 1 1 1] [1 1 0 1 1 1 1] [1 0 0 0 1 1 1] }}} {{{id=26| G958=Matrix([[0,1,1,-2,1,1,0],[1,1,1,0,0,0,1],[1,1,1,0,0,0,1],[-2,0,0,-2,0,0,- 2],[1,0,0,0,1,1,1],[1,0,0,0,1,1,1],[0,1,1,-2,1,1,0]]) check_witness(G958,958) /// Rank is 3 Symmetric? True Isomorphic to graph G 958 True [ 0 1 1 -2 1 1 0] [ 1 1 1 0 0 0 1] [ 1 1 1 0 0 0 1] [-2 0 0 -2 0 0 -2] [ 1 0 0 0 1 1 1] [ 1 0 0 0 1 1 1] [ 0 1 1 -2 1 1 0] }}} {{{id=27| G970=Matrix([[1,1,1,0,0,0,0],[1,2,2,1,1,0,0],[1,2,1,1,0,-1,-1],[0,1,1,1,1,0,0],[0,1,0,1,0,-1,-1],[0,0,-1,0,-1,-1,-1],[0,0,-1,0,-1,-1,-1]]) check_witness(G970,970) /// Rank is 3 Symmetric? True Isomorphic to graph G 970 True [ 1 1 1 0 0 0 0] [ 1 2 2 1 1 0 0] [ 1 2 1 1 0 -1 -1] [ 0 1 1 1 1 0 0] [ 0 1 0 1 0 -1 -1] [ 0 0 -1 0 -1 -1 -1] [ 0 0 -1 0 -1 -1 -1] }}} {{{id=83| G990=Matrix([[1/8,1/2,0,1/2,0,0,0],[1/2,0,2,1,1,0,0],[0,2,-1,1,0,1,1],[1/2,1,1,3/2,1/2,0,0],[0,1,0,1/2,1/2,1,1],[0,0,1,0,1,1,1],[0,0,1,0,1,1,1]]) check_witness(G990,990) /// Rank is 3 Symmetric? True Isomorphic to graph G 990 True [1/8 1/2 0 1/2 0 0 0] [1/2 0 2 1 1 0 0] [ 0 2 -1 1 0 1 1] [1/2 1 1 3/2 1/2 0 0] [ 0 1 0 1/2 1/2 1 1] [ 0 0 1 0 1 1 1] [ 0 0 1 0 1 1 1] }}} {{{id=84| G995=Matrix([[1,1,0,1,1,0,0],[1,1,1,0,0,1,1],[0,1,-1,1,2,0,0],[1,0,1,0,-1,0,0],[1,0,2,-1,-2,1,1],[0,1,0,0,1,1,1],[0,1,0,0,1,1,1]]) check_witness(G995,995) /// Rank is 3 Symmetric? True Isomorphic to graph G 995 True [ 1 1 0 1 1 0 0] [ 1 1 1 0 0 1 1] [ 0 1 -1 1 2 0 0] [ 1 0 1 0 -1 0 0] [ 1 0 2 -1 -2 1 1] [ 0 1 0 0 1 1 1] [ 0 1 0 0 1 1 1] }}} {{{id=85| G996=Matrix([[1,0,1,0,1,0,1],[0,2,1,1,0,2,0],[1,1,1,0,2,1,1],[0,1,0,0,1,1,0],[1,0,2,1,-1,0,1],[0,2,1,1,0,2,0],[1,0,1,0,1,0,1]]) check_witness(G996,996) /// Rank is 3 Symmetric? True Isomorphic to graph G 996 True [ 1 0 1 0 1 0 1] [ 0 2 1 1 0 2 0] [ 1 1 1 0 2 1 1] [ 0 1 0 0 1 1 0] [ 1 0 2 1 -1 0 1] [ 0 2 1 1 0 2 0] [ 1 0 1 0 1 0 1] }}} {{{id=81| G1002=Matrix([[1,0,1,1,0,0,1],[0,0,1,1,-1,-1,0],[1,1,1,0,0,-1,1],[1,1,0,-1,1,0,1],[0,-1,0,1,0,1,0],[0,-1,-1,0,1,2,0],[1,0,1,1,0,0,1]]) check_witness(G1002,1002) /// Rank is 3 Symmetric? True Isomorphic to graph G 1002 True [ 1 0 1 1 0 0 1] [ 0 0 1 1 -1 -1 0] [ 1 1 1 0 0 -1 1] [ 1 1 0 -1 1 0 1] [ 0 -1 0 1 0 1 0] [ 0 -1 -1 0 1 2 0] [ 1 0 1 1 0 0 1] }}} {{{id=79| G1005=matrix( [(1, 0, 0, 0, 1, 1, 1), (0, 1, 0, 1, 0, -1, 1), (0, 0, 1, 1, 1, 0, -1), (0, 1, 1, 2, 1,-1, 0), (1, 0, 1,1, 2, 1, 0), (1,-1, 0, -1, 1, 2, 0), (1,1, -1, 0, 0, 0, 3)]) check_witness(G1005,1005) /// Rank is 3 Symmetric? True Isomorphic to graph G 1005 True [ 1 0 0 0 1 1 1] [ 0 1 0 1 0 -1 1] [ 0 0 1 1 1 0 -1] [ 0 1 1 2 1 -1 0] [ 1 0 1 1 2 1 0] [ 1 -1 0 -1 1 2 0] [ 1 1 -1 0 0 0 3] }}} {{{id=86| G1028=Matrix([[1,0,2,-1,1,1,0],[0,0,1,0,1,0,0],[2,1,4,-1,2,2,1],[-1,0,-1,1,0,-1,0],[1,1,2,0,1,1,1],[1,0,2,-1,1,1,0],[0,0,1,0,1,0,0]]) check_witness(G1028,1028) /// Rank is 3 Symmetric? True Isomorphic to graph G 1028 True [ 1 0 2 -1 1 1 0] [ 0 0 1 0 1 0 0] [ 2 1 4 -1 2 2 1] [-1 0 -1 1 0 -1 0] [ 1 1 2 0 1 1 1] [ 1 0 2 -1 1 1 0] [ 0 0 1 0 1 0 0] }}} {{{id=87| G1060=Matrix([[2,-1,-1,0,1,1,0],[-1,2,1,1,1,0,1],[-1,1,1,0,0,0,1],[0,1,0,1,1,0,0],[1,1,0,1,2,1,1],[1,0,0,0,1,1,1],[0,1,1,0,1,1,2]]) check_witness(G1060,1060) /// Rank is 3 Symmetric? True Isomorphic to graph G 1060 True [ 2 -1 -1 0 1 1 0] [-1 2 1 1 1 0 1] [-1 1 1 0 0 0 1] [ 0 1 0 1 1 0 0] [ 1 1 0 1 2 1 1] [ 1 0 0 0 1 1 1] [ 0 1 1 0 1 1 2] }}} {{{id=88| G1075=Matrix([[0,-1,2,1,2,0,0],[-1,0,1,0,0,1,-1],[2,1,0,1,0,0,2],[1,0,1,1,1,0,1],[2,0,0,1,1,-1,2],[0,1,0,0,-1,1,0],[0,-1,2,1,2,0,0]]) check_witness(G1075,1075) /// Rank is 3 Symmetric? True Isomorphic to graph G 1075 True [ 0 -1 2 1 2 0 0] [-1 0 1 0 0 1 -1] [ 2 1 0 1 0 0 2] [ 1 0 1 1 1 0 1] [ 2 0 0 1 1 -1 2] [ 0 1 0 0 -1 1 0] [ 0 -1 2 1 2 0 0] }}} {{{id=89| G1077=Matrix([[0,0,1,1,1,0,0],[0,1,0,-1,-1,0,1],[1,0,1,1,0,1,0],[1,-1,1,2,1,1,-1],[1,-1,0,1,0,1,-1],[0,0,1,1,1,0,0],[0,1,0,-1,-1,0,1]]) check_witness(G1077,1077) /// Rank is 3 Symmetric? True Isomorphic to graph G 1077 True [ 0 0 1 1 1 0 0] [ 0 1 0 -1 -1 0 1] [ 1 0 1 1 0 1 0] [ 1 -1 1 2 1 1 -1] [ 1 -1 0 1 0 1 -1] [ 0 0 1 1 1 0 0] [ 0 1 0 -1 -1 0 1] }}} {{{id=90| G1087=Matrix([[0,0,1,1,1,0,0],[0,1,1,0,1,1,0],[1,1,0,-1,0,1,1],[1,0,-1,-1,-1,0,1],[1,1,0,-1,0,1,1],[0,1,1,0,1,1,0],[0,0,1,1,1,0,0]]) check_witness(G1087,1087) /// Rank is 3 Symmetric? True Isomorphic to graph G 1087 True [ 0 0 1 1 1 0 0] [ 0 1 1 0 1 1 0] [ 1 1 0 -1 0 1 1] [ 1 0 -1 -1 -1 0 1] [ 1 1 0 -1 0 1 1] [ 0 1 1 0 1 1 0] [ 0 0 1 1 1 0 0] }}} {{{id=80| G1095=matrix( [(2,1,0,0,1,-1,-1), (1,2,1,0,0,-1,2), (0,1,1,1,0,0,2), (0,0,1,3,1,1,1), (1,0,0,1,1,0,-1), (-1,-1,0,1,0,1,0), (-1,2,2,1,-1,0,5)]) check_witness(G1095,1095) /// Rank is 3 Symmetric? True Isomorphic to graph G 1095 True [ 2 1 0 0 1 -1 -1] [ 1 2 1 0 0 -1 2] [ 0 1 1 1 0 0 2] [ 0 0 1 3 1 1 1] [ 1 0 0 1 1 0 -1] [-1 -1 0 1 0 1 0] [-1 2 2 1 -1 0 5] }}} {{{id=91| G1099=Matrix([[1,0,1,0,1,0,1],[0,2,1,1,0,2,0],[1,1,1,0,2,1,2],[0,1,0,0,1,1,1],[1,0,2,1,-1,0,-1],[0,2,1,1,0,2,0],[1,0,2,1,-1,0,-1]]) check_witness(G1099,1099) /// Rank is 3 Symmetric? True Isomorphic to graph G 1099 True [ 1 0 1 0 1 0 1] [ 0 2 1 1 0 2 0] [ 1 1 1 0 2 1 2] [ 0 1 0 0 1 1 1] [ 1 0 2 1 -1 0 -1] [ 0 2 1 1 0 2 0] [ 1 0 2 1 -1 0 -1] }}} {{{id=0| G1104=matrix( [(-1,2,2,3,0,0,0), (2,-1,2,0,3,0,3), (2,2,-1,0,0,3,-3), (3,0,0,-1,2,2,0), (0,3,0,2,-1,2,-3), (0,0,3,2,2,-1,3), (0,3,-3,0,-3,3,-6)]) check_witness(G1104,1104) /// Rank is 3 Symmetric? True Isomorphic to graph G 1104 True [-1 2 2 3 0 0 0] [ 2 -1 2 0 3 0 3] [ 2 2 -1 0 0 3 -3] [ 3 0 0 -1 2 2 0] [ 0 3 0 2 -1 2 -3] [ 0 0 3 2 2 -1 3] [ 0 3 -3 0 -3 3 -6] }}} {{{id=76| G1146=matrix([[-1,1,0,0,-1,0,-3],[1,-2,1,0,1,-1,4], [0,1,-2,1,1,1,-4],[0,0,1,-1,-1,0,3],[-1,1,1,-1,-2,0,0],[0,-1,1,0,0,-1,1],[-3,4,-4,3,0,1,-19]]) check_witness(G1146,1146) /// Rank is 3 Symmetric? True Isomorphic to graph G 1146 True [ -1 1 0 0 -1 0 -3] [ 1 -2 1 0 1 -1 4] [ 0 1 -2 1 1 1 -4] [ 0 0 1 -1 -1 0 3] [ -1 1 1 -1 -2 0 0] [ 0 -1 1 0 0 -1 1] [ -3 4 -4 3 0 1 -19] }}} {{{id=29| G1167=Matrix([[0,1,0,0,1,2,1],[1,-1,1,0,0,-1,-1],[0,1,-1,1,0,1,2],[0,0,1,- 1,1,1,-1],[1,0,0,1,0,0,1],[2,-1,1,1,0,-1,0],[1,-1,2,-1,1,0,-2]]) check_witness(G1167,1167) /// Rank is 3 Symmetric? True Isomorphic to graph G 1167 True [ 0 1 0 0 1 2 1] [ 1 -1 1 0 0 -1 -1] [ 0 1 -1 1 0 1 2] [ 0 0 1 -1 1 1 -1] [ 1 0 0 1 0 0 1] [ 2 -1 1 1 0 -1 0] [ 1 -1 2 -1 1 0 -2] }}} {{{id=34| G1205=matrix( [(3/5, 1/10, -1/2,0,1,1,0), (1/10, 3/5, 1/2,1,0,1,0), (-1/2, 1/2, 1,1,-1,0,0), (0, 1, 1,3, 1, 1,3), (1, 0, -1,1, 3, 1,3), (1, 1, 0,1, 1, 3,-1), (0,0,0,3,3,-1,7)]) check_witness(G1205,1205) /// Rank is 3 Symmetric? True Isomorphic to graph G 1205 True [ 3/5 1/10 -1/2 0 1 1 0] [1/10 3/5 1/2 1 0 1 0] [-1/2 1/2 1 1 -1 0 0] [ 0 1 1 3 1 1 3] [ 1 0 -1 1 3 1 3] [ 1 1 0 1 1 3 -1] [ 0 0 0 3 3 -1 7] }}} {{{id=93| G1212=Matrix([(0, 4, -2, 3, 2, 1, 0), (4, -1, 1, 0, 0, 1, 4), (-2, 1, -1, 1, 0, 0, -2), (3, 0, 1, -1, 1, 0, 3), (2, 0, 0, 1, 0, 1, 2), (1, 1, 0, 0, 1, 0, 1), (0, 4, -2, 3, 2, 1, 0)]) check_witness(G1212,1212) /// Rank is 3 Symmetric? True Isomorphic to graph G 1212 True [ 0 4 -2 3 2 1 0] [ 4 -1 1 0 0 1 4] [-2 1 -1 1 0 0 -2] [ 3 0 1 -1 1 0 3] [ 2 0 0 1 0 1 2] [ 1 1 0 0 1 0 1] [ 0 4 -2 3 2 1 0] }}} {{{id=94| /// }}}