5-chord.nb

k = 0;
Clear[t1, t2, t3, t4, t5, P];
at = ConstantArray[0, 10];
at[[1]] = 1;
For[l1 = 2, l1 < 11, l1++,
  at[[l1]] = 1;
      t1[1, l1] = {1, l1};
  If[l1 == 2, l2 = 3, l2 = 2];
  at[[l2]] = 1;
      For [l3 = l2 + 1, l3 < 11, l3++,
       If [l3 != l1,
     at[[l3]] = 1;
           t2[l2, l3] = {l2, l3};
     it = 0;
     at[[l1]] = 1; at[[l2]] = 1; at[[l3]] = 1;
     For  [kt = 1, kt < 11, kt++,
      If [it == 0, l4 = kt];
      If[at[[kt]] == 0, it = 1];
      ];
     at[[l4]] = 1;
     For [l5 = l4 + 1, l5 < 11, l5++,
          If [l5 != l1 && l5 != l2 && l5 != l3,
              t3[l4, l5] = {l4, l5};
        at[[l1]] = 1; at[[l2]] = 1; at[[l3]] = 1; at[[l4]] = 1; 
        at[[l5]] = 1;
        it = 0;
        (**Print[at[[1]],at[[2]],at[[3]],at[[4]],at[[5]],at[[6]],at[[
        7]]];**)
        For  [kt = 1, kt < 11, kt++,
         If [it == 0, l6 = kt];
         If[at[[kt]] == 0, it = 1];
         ];
        at[[l6]] = 1;
        For [l7 = l6 + 1, l7 < 11, l7++,
             
         If [l7 != l1 && l7 != l2 && l7 != l3 && l7 != l4 && 
            l7 != l5,
                 t4[l6, l7] = {l6, l7};
           at[[l1]] = 1; at[[l2]] = 1; at[[l3]] = 1; at[[l4]] = 1; 
           at[[l5]] = 1; at[[l6]] = 1; at[[l7]] = 1;
           it = 0;
           For  [kt = 1, kt < 11, kt++,
            If [it == 0, l8 = kt];
            If[at[[kt]] == 0, it = 1];
            ];
           at[[l8]] = 1;
           For [l9 = l8 + 1, l9 < 11, l9++,
                
            If [l9 != l1 && l9 != l2 && l9 != l3 && l9 != l4 && 
               l9 != l5 && l9 != l6 && l9 != l7,
                    t5[l8, l9] = {l8, l9};
              k = k + 1;
              (**Print[" k = ",k,"  ", l1,l2,l3,l4,l5,l6,l7];**)
     
                       
              Pairs[k] = {t1[1, l1], t2[l2, l3], t3[l4, l5], 
                t4[l6, l7], t5[l8, l9]};
              at = ConstantArray[0, 10]; at[[1]] = 1;
              ];];];];];];];];];

adj = ConstantArray[0, {945, 5, 5}];(*adjacency matrix*)

edgeAndtriangle = 
  ConstantArray[
   0, {945, 1, 2}];(*list of {# of edges, # of triangles}*)
For[c = 1,
  c < 946, c++,
 For[i = 1, i < 6, i++,
  For[j = i + 1, j < 6, j++,
    crossingtemp = 0;
    temp1 = Pairs[c][[i]][[2]];
    temp2 = Pairs[c][[j]][[1]];
    temp3 = Pairs[c][[j]][[2]];
    If[temp1 > temp2, crossingtemp = crossingtemp + 1];
    If[temp1 > temp3, crossingtemp = crossingtemp + 1];
    crossingtemp = Mod[crossingtemp, 2];
    adj[[c, i, j]] = crossingtemp;
    ];];
 adj[[c]] = adj[[c]] + Transpose[adj[[c]]];
 edgeAndtriangle[[c]] = {1/2 Tr[adj[[c]].adj[[c]]], 
   1/6 Tr[adj[[c]].adj[[c]].adj[[c]]]}; 
 ]


EandTstat = Table[{e, 0}, {e, 0, 10}]; For[c = 1, c < 946, c++,
 e = edgeAndtriangle[[c, 1]];
 t = edgeAndtriangle[[c, 2]];
 EandTstat[[e + 1, 2]] = EandTstat[[e + 1, 2]] + t;]

EandTstat

{{0, 0}, {1, 0}, {2, 0}, {3, 45}, {4, 90}, {5, 135}, {6, 140}, {7, 
  105}, {8, 70}, {9, 35}, {10, 10}}

evencount = 0;
oddcount = 0;
Do[evencount = evencount + EandTstat[[i, 2]], {i, 1, 11, 2}]
Do[oddcount = oddcount + EandTstat[[i, 2]], {i, 2, 11, 2}]
evencount
oddcount

310

320