# #############################################################################
# Question Mark Computing Perception 
# Copyright (c) Question Mark Computing Ltd. 1998 - 2001
# 
# LOCAL.FORMAT version 3.1.0
# all user defined settings
# #############################################################################

[DOCUMENT]







GRAPHTHEORY_QUESTIONS=
<script>


// ______________________________________________________________________________________


function SVG_network(A,weights,arrow_ratio_along_line,filled,weights_ratio_along_line,weights_font_colour,weights_font_scale){

NRC = MatrixSize(A);
var n = NRC[0];

var fs = getFontSize()/16;

if(weights_font_colour == null){weights_font_colour = getFgColor();}
if(weights_font_scale == null){weights_font_scale = fs;}


size1 = fs*800;
size2 = fs*800;
size3 = fs*(100*fs*fs+410*fs+250);
size4 = fs*(100*fs*fs+410*fs+200);

    svg_start = '<iSvg:svg height="'+size1+'" width="'+size2+'" viewBox="0 0 '+size3+' '+size4+'"><iSvg:g id="canvas">';
    svg_end = '<iSvg:g></iSvg:svg>';

SVG_graph = "";

r = getFontSize()/16*200;
rrloop = getFontSize()/16*50;
rloop = r + rrloop

offset = r+getFontSize()/16*200;
offset2 = r+getFontSize()/16*75;

x_coord = new Array(n);
y_coord = new Array(n);
x_coord_loop = new Array(n);
y_coord_loop = new Array(n);
x_coord_label = new Array(n);
y_coord_label = new Array(n);

for(k = 0; k <= n-1; k++){
   x_coord[k] = r*Math.cos(2*k*Math.PI/n)+offset;
   y_coord[k] = r*Math.sin(2*k*Math.PI/n)+offset;
   x_coord_label[k] = (r+offset2)/2*Math.cos(2*k*Math.PI/n)+(offset);
   y_coord_label[k] = (r+offset2)/2*Math.sin(2*k*Math.PI/n)+offset;
   x_coord_loop[k] = rloop*Math.cos(2*k*Math.PI/n)+offset;
   y_coord_loop[k] = rloop*Math.sin(2*k*Math.PI/n)+offset;
}


var colour = getFgColor();



for(i = 1; i <= n; i++) {
   SVG_graph += SVG_ellipsebl(x_coord[i-1],y_coord[i-1],0.1,0.1)+SVG_scale_text(x_coord_label[i-1],y_coord_label[i-1],alphabet(i-1,1),colour,fs);

      for(j = 1; j <= n; j++){
         if(A[i][j] == 1){

if(arrow_ratio_along_line != 0){
SVG_graph += SVG_arrow(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1],arrow_ratio_along_line,filled);}

else{
SVG_graph += SVG_line(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1])};

      }

   }

// ///////////////// bit for loops on a vertex



         if(A[i][i] != 0){

            SVG_graph += SVG_ellipse(x_coord_loop[i-1],y_coord_loop[i-1],rrloop,rrloop);
      }
}

// ///////////////// lastly add the network weights so that they are always on top and hence legible


for(i = 1; i <= n; i++) {
      for(j = 1; j <= n; j++){
         if(A[i][j] != 0){
x1 = x_coord[i-1];
x2 = x_coord[j-1];
y1 = y_coord[i-1];
y2 = y_coord[j-1];
var length_of_line = Math.pow((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2),0.5);
var angle_of_line = angle_from_xy(x2-x1,y2-y1);

var xtext = x1*(1-weights_ratio_along_line)+x2*weights_ratio_along_line;
var ytext = y1*(1-weights_ratio_along_line)+y2*weights_ratio_along_line;
if(weights_ratio_along_line != 0){SVG_graph += SVG_scale_text(xtext,ytext,weights[i][j],weights_font_colour,weights_font_scale*fs)};
      }

   }
}

return svg_start + SVG_graph + svg_end;
}


/////////////////////////////////////////////////////////////////////////////////////////////////////////
//___________________________________________________________________________________________________________________________


function SVG_digraph(A,ratio_along_line,filled,double_path_colour,double_path_skinnyness,svg_start){

if(double_path_skinnyness == null){double_path_skinnyness = 10};

NRC = MatrixSize(A);
var n = NRC[0];


var fs = getFontSize()/16;
size1 = fs*800;
size2 = fs*800;
size3 = fs*(100*fs*fs+410*fs+250);
size4 = fs*(100*fs*fs+410*fs+200);


if(svg_start == null){svg_start = '<iSvg:svg height="'+size1+'" width="'+size2+'" viewBox="0 0 '+size3+' '+size4+'"><iSvg:g id="canvas">';}
    svg_end = '<iSvg:g></iSvg:svg>';

SVG_graph = "";

r = fs*200;
rrloop = fs*50;
rloop = r + rrloop

offset = r+fs*200;
offset2 = r+fs*75;

x_coord = new Array(n);
y_coord = new Array(n);
x_coord_loop = new Array(n);
y_coord_loop = new Array(n);
x_coord_label = new Array(n);
y_coord_label = new Array(n);

for(k = 0; k <= n-1; k++){
   x_coord[k] = r*Math.cos(2*k*Math.PI/n)+offset;
   y_coord[k] = r*Math.sin(2*k*Math.PI/n)+offset;
   x_coord_label[k] = (r+offset2)/2*Math.cos(2*k*Math.PI/n)+(offset);
   y_coord_label[k] = (r+offset2)/2*Math.sin(2*k*Math.PI/n)+(offset);
   x_coord_loop[k] = rloop*Math.cos(2*k*Math.PI/n)+offset;
   y_coord_loop[k] = rloop*Math.sin(2*k*Math.PI/n)+offset;
}

colour = getFgColor();
for(i = 1; i <= n; i++) {
   SVG_graph += SVG_ellipsebl(x_coord[i-1],y_coord[i-1],0.1,0.1)+SVG_scale_text(x_coord_label[i-1],y_coord_label[i-1],alphabet(i-1,1),colour,fs);

      for(j = 1; j <= n; j++){

         if(A[i][j] == 1){
if(ratio_along_line != 0){SVG_graph += SVG_arrow(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1],ratio_along_line,filled)}else{
SVG_graph += SVG_line(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1])};
      }

   if(A[i][j] == 2){
cxx = (x_coord[i-1]+x_coord[j-1])/2;
cyy = (y_coord[i-1]+y_coord[j-1])/2;
dx = (x_coord[i-1]-x_coord[j-1]);
dy = (y_coord[i-1]-y_coord[j-1]);
if(dx == 0){theta = 90}else{theta = Math.atan(dy/dx)*180/Math.PI};
rxx = Math.pow((x_coord[i-1]-x_coord[j-1])*(x_coord[i-1]-x_coord[j-1])+(y_coord[i-1]-y_coord[j-1])*(y_coord[i-1]-y_coord[j-1]),0.5)/2;
ryy = rxx/double_path_skinnyness; // gives a skinny ellipse
SVG_graph += SVG_ellipse_rotate(cxx,cyy,rxx,ryy,theta,double_path_colour);
      }

   }
// ///////////////// bit for loops on a vertex



         if(A[i][i] != 0){

            SVG_graph += SVG_ellipse(x_coord_loop[i-1],y_coord_loop[i-1],rrloop,rrloop);
      }

// /////////////////



}



return svg_start + SVG_graph + svg_end;
}


//______________________________________________________________

//___________________________________________________________________________________________________________________________

function SVG_digraph_label(A,labels,ratio_along_line,filled,double_path_colour,double_path_skinnyness,svg_start){

if(double_path_skinnyness == null){double_path_skinnyness = 10};

NRC = MatrixSize(A);
var n = NRC[0];

var fs = getFontSize()/16;
size1 = fs*800;
size2 = fs*800;
size3 = fs*(100*fs*fs+410*fs+250);
size4 = fs*(100*fs*fs+410*fs+200);

if(svg_start == null){svg_start = '<iSvg:svg height="'+size1+'" width="'+size2+'" viewBox="0 0 '+size3+' '+size4+'"><iSvg:g id="canvas">';}
    svg_end = '<iSvg:g></iSvg:svg>';

SVG_graph = "";

r = getFontSize()/16*150;
rrloop = getFontSize()/16*50;
rloop = r + rrloop

offset = r+getFontSize()/16*200;
offset2 = r+getFontSize()/16*75;

x_coord = new Array(n);
y_coord = new Array(n);
x_coord_loop = new Array(n);
y_coord_loop = new Array(n);
x_coord_label = new Array(n);
y_coord_label = new Array(n);

for(k = 0; k <= n-1; k++){
   x_coord[k] = r*Math.cos(2*k*Math.PI/n)+offset;
   y_coord[k] = r*Math.sin(2*k*Math.PI/n)+offset;
   x_coord_label[k] = ((1.4*r)+offset2)/2*Math.cos(2*k*Math.PI/n)+(0.9*offset);
   y_coord_label[k] = ((1.4*r)+offset2)/2*Math.sin(2*k*Math.PI/n)+(offset);
   x_coord_loop[k] = rloop*Math.cos(2*k*Math.PI/n)+offset;
   y_coord_loop[k] = rloop*Math.sin(2*k*Math.PI/n)+offset;
}

colour = getFgColor();
for(i = 1; i <= n; i++) {
   SVG_graph += SVG_ellipsebl(x_coord[i-1],y_coord[i-1],0.1,0.1)+SVG_scale_text(x_coord_label[i-1],y_coord_label[i-1],labels[i],colour,fs);

      for(j = 1; j <= n; j++){

         if(A[i][j] == 1){
if(ratio_along_line != 0){SVG_graph += SVG_arrow(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1],ratio_along_line,filled)}else{
SVG_graph += SVG_line(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1])};
      }

   if(A[i][j] == 2){
cxx = (x_coord[i-1]+x_coord[j-1])/2;
cyy = (y_coord[i-1]+y_coord[j-1])/2;
dx = (x_coord[i-1]-x_coord[j-1]);
dy = (y_coord[i-1]-y_coord[j-1]);
if(dx == 0){theta = 90}else{theta = Math.atan(dy/dx)*180/Math.PI};
rxx = Math.pow((x_coord[i-1]-x_coord[j-1])*(x_coord[i-1]-x_coord[j-1])+(y_coord[i-1]-y_coord[j-1])*(y_coord[i-1]-y_coord[j-1]),0.5)/2;
ryy = rxx/double_path_skinnyness; // gives a skinny ellipse
SVG_graph += SVG_ellipse_rotate(cxx,cyy,rxx,ryy,theta,double_path_colour);
      }

   }
// ///////////////// bit for loops on a vertex



         if(A[i][i] != 0){

            SVG_graph += SVG_ellipse(x_coord_loop[i-1],y_coord_loop[i-1],rrloop,rrloop);
      }

// /////////////////



}



return svg_start + SVG_graph + svg_end;
}

//___________________________________________________________________________________________________________________________

//function SVG_digraph_label_colours(A,labels,ratio_along_line,filled,double_path_colour,vertex_colours,numeric_order,double_path_skinnyness,vertex_radius,svg_start)
//If labels == 0, then alphabetical order is given to the labels.
//If you want large, coloured vertices to appear, then set vertex_radius = 10. Otheriwse, set vertex_radius = 0.1.

function SVG_digraph_label_colours(A,labels,ratio_along_line,filled,double_path_colour,vertex_colours,numeric_order,double_path_skinnyness,vertex_radius,svg_start){

if(double_path_skinnyness == null){double_path_skinnyness = 10};

NRC = MatrixSize(A);
var n = NRC[0];

substituted_labels = new Array();
if(labels == 0){
   for(i = 1; i <= n; i++){
      substituted_labels[i] = alphabet(i-1,1);
   }
}else{
   for(i = 1; i <= n; i++){
      substituted_labels[i] = labels[i];
   }
}

var fs = getFontSize()/16;
size1 = fs*800;
size2 = fs*800;
size3 = fs*(100*fs*fs+410*fs+250);
size4 = fs*(100*fs*fs+410*fs+200);

if(svg_start == null){svg_start = '<iSvg:svg height="'+size1+'" width="'+size2+'" viewBox="0 0 '+size3+' '+size4+'"><iSvg:g id="canvas">';}
    svg_end = '<iSvg:g></iSvg:svg>';

SVG_graph = "";

r = getFontSize()/16*150;
rrloop = getFontSize()/16*50;
rloop = r + rrloop;

offset = r+getFontSize()/16*200;
offset2 = r+getFontSize()/16*75;

x_coord = new Array(n);
y_coord = new Array(n);
x_coord_loop = new Array(n);
y_coord_loop = new Array(n);
x_coord_label = new Array(n);
y_coord_label = new Array(n);

for(k = 0; k <= n-1; k++){
   x_coord[k] = r*Math.cos(2*k*Math.PI/n)+offset;
   y_coord[k] = r*Math.sin(2*k*Math.PI/n)+offset;
   x_coord_label[k] = ((1.4*r)+offset2)/2*Math.cos(2*k*Math.PI/n)+(0.9*offset);
   y_coord_label[k] = ((1.4*r)+offset2)/2*Math.sin(2*k*Math.PI/n)+(offset);
   x_coord_loop[k] = rloop*Math.cos(2*k*Math.PI/n)+offset;
   y_coord_loop[k] = rloop*Math.sin(2*k*Math.PI/n)+offset;
}

colour = getFgColor();

for(i = 1; i <= n; i++) {
   
      for(j = 1; j <= n; j++){

         if(A[i][j] == 1){
if(ratio_along_line != 0){SVG_graph += SVG_arrow(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1],ratio_along_line,filled)}else{
SVG_graph += SVG_line(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1])};
      }

   if(A[i][j] == 2){
cxx = (x_coord[i-1]+x_coord[j-1])/2;
cyy = (y_coord[i-1]+y_coord[j-1])/2;
dx = (x_coord[i-1]-x_coord[j-1]);
dy = (y_coord[i-1]-y_coord[j-1]);
if(dx == 0){theta = 90}else{theta = Math.atan(dy/dx)*180/Math.PI};
rxx = Math.pow((x_coord[i-1]-x_coord[j-1])*(x_coord[i-1]-x_coord[j-1])+(y_coord[i-1]-y_coord[j-1])*(y_coord[i-1]-y_coord[j-1]),0.5)/2;
ryy = rxx/double_path_skinnyness; // gives a skinny ellipse
SVG_graph += SVG_ellipse_rotate(cxx,cyy,rxx,ryy,theta,double_path_colour);
      }

   }
// ///////////////// bit for loops on a vertex



         if(A[i][i] != 0){

            SVG_graph += SVG_ellipse(x_coord_loop[i-1],y_coord_loop[i-1],rrloop,rrloop);
      }
}

for(i = 1; i <= n; i++) {
SVG_graph += SVG_ellipseblx(x_coord[i-1],y_coord[i-1],vertex_radius,vertex_radius,vertex_colours[(numeric_order[i-1]-0)-1])+SVG_scale_text(x_coord_label[i-1],y_coord_label[i-1],substituted_labels[i],colour,fs);
}

return svg_start + SVG_graph + svg_end;
}


//______________________________________________________________

//function graphiccheck
//If graphiccheck = 0, then the sequence is non-graphic.
//If graphiccheck = 1, then the sequence is graphic.

function graphiccheck(sequence){

degree = new Array();
degree = sorting(sequence,0);
n = degree.length;

graphiccheck1 = 0;
summation = 0;
for(i = 0; i <= n-1; i++){
   summation += (degree[i]-0);
}
if(summation%2 == 1%2){
   graphiccheck1 += 1;
}

pivot = (degree[0]-0);
LS = new Array();
RS = new Array();
graphiccheck2 = 0;

for(i = 0; i <= pivot-1; i++){
   for(j = 0; j <= i; j++){
      LS[i] = 0;
      LS[i] += degree[j];
   }
   for(k = i+1; k <= n; k++){
      RS[i] = i*(i+1);
      RS[i] += Math.min(i,degree[k]);
   }
   if(LS[i] > RS[i]){
      graphiccheck2 += 1;
   }
}

if(graphiccheck1 > 0){
   return "0"
}else if(graphiccheck2 > 0){
   return "0"
}else{
   return "1"
}

}

//___________________________________________________________________________________________________________________________

function SVG_wheelgraph(rows,ratio_along_line,filled,double_path_colour,double_path_skinnyness,svg_start){


A = getrandommatrix(rows, rows, 0, 0, 1);
Dis = getrandommatrix(rows, rows, 0, 0, 1);

for (i = 1; i <= rows-2; i++){
   A[i][i+1] = (A[i][i+1]-0)+1;
}
A[rows-1][1] = (A[rows-1][1]-0)+1;
for(i = 1; i <= rows-1; i++){
  A[i][rows] = (A[i][rows]-0)+1;
} 

for(i = 1; i <= rows; i++){
   for(j = i; j <= rows; j++){
      Dis[i][j] = Math.max((A[i][j]-0),(A[j][i]-0));
      Dis[j][i] = Math.max((A[i][j]-0),(A[j][i]-0));
   }
}


if(double_path_skinnyness == null){double_path_skinnyness = 10};

NRC = MatrixSize(Dis);
var n1 = NRC[0] - 1;
var n = NRC[0];

var fs = getFontSize()/16;
size1 = fs*950;
size2 = fs*1100;
size3 = fs*(100*fs*fs+410*fs+250);
size4 = fs*(100*fs*fs+410*fs+200);

if(svg_start == null){svg_start = '<iSvg:svg height="'+size1+'" width="'+size2+'" viewBox="0 0 '+size3+' '+size4+'"><iSvg:g id="canvas">';}
    svg_end = '<iSvg:g></iSvg:svg>';

SVG_graph = "";

r = getFontSize()/16*150;
rrloop = getFontSize()/16*50;
rloop = r + rrloop

offset = r+getFontSize()/16*150;
offset2 = r+getFontSize()/16*75;

x_coord = new Array(n);
y_coord = new Array(n);
x_coord_loop = new Array(n);
y_coord_loop = new Array(n);
x_coord_label = new Array(n);
y_coord_label = new Array(n);

for(k = 0; k <= n1-1; k++){
   x_coord[k] = r*Math.cos(2*k*Math.PI/n1)+offset;
   y_coord[k] = r*Math.sin(2*k*Math.PI/n1)+offset;
   x_coord_label[k] = ((1.4*r)+offset2)/2*Math.cos(2*k*Math.PI/n1)+(0.9*offset);
   y_coord_label[k] = ((1.4*r)+offset2)/2*Math.sin(2*k*Math.PI/n1)+(offset);
   x_coord_loop[k] = rloop*Math.cos(2*k*Math.PI/n1)+offset;
   y_coord_loop[k] = rloop*Math.sin(2*k*Math.PI/n1)+offset;
}
   x_coord[n-1] = offset;
   y_coord[n-1] = offset;
   x_coord_label[n-1] = (r/5)+offset;
   y_coord_label[n-1] = (r/5)*Math.sin(2*Math.PI/n1)+offset;
   x_coord_loop[n-1] = offset;
   y_coord_loop[n-1] = offset;

colour = getFgColor();

//SVG_graph += SVG_ellipsebl(x_coord[n-1],y_coord[n-1],0.1,0.1)+SVG_scale_text(x_coord_label[n-1],y_coord_label[n-1],"",colour,fs);

for(i = 1; i <= n; i++) {
   SVG_graph += SVG_ellipsebl(x_coord[i-1],y_coord[i-1],0.1,0.1)+SVG_scale_text(x_coord_label[i-1],y_coord_label[i-1],alphabet([i-1],1),colour,fs);

      for(j = 1; j <= n; j++){

         if(A[i][j] == 1){
if(ratio_along_line != 0){SVG_graph += SVG_arrow(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1],ratio_along_line,filled)}else{
SVG_graph += SVG_line(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1])};
      }

   if(A[i][j] == 2){
cxx = (x_coord[i-1]+x_coord[j-1])/2;
cyy = (y_coord[i-1]+y_coord[j-1])/2;
dx = (x_coord[i-1]-x_coord[j-1]);
dy = (y_coord[i-1]-y_coord[j-1]);
if(dx == 0){theta = 90}else{theta = Math.atan(dy/dx)*180/Math.PI};
rxx = Math.pow((x_coord[i-1]-x_coord[j-1])*(x_coord[i-1]-x_coord[j-1])+(y_coord[i-1]-y_coord[j-1])*(y_coord[i-1]-y_coord[j-1]),0.5)/2;
ryy = rxx/double_path_skinnyness; // gives a skinny ellipse
SVG_graph += SVG_ellipse_rotate(cxx,cyy,rxx,ryy,theta,double_path_colour);
      }

   }
// ///////////////// bit for loops on a vertex



         if(A[i][i] != 0){

            SVG_graph += SVG_ellipse(x_coord_loop[i-1],y_coord_loop[i-1],rrloop,rrloop);
      }

// /////////////////



}



return svg_start + SVG_graph + svg_end;
}

//___________________________________________________________________________________________________________________________

function SVG_wheelgraph_label(rows,labels,ratio_along_line,filled,double_path_colour,double_path_skinnyness,svg_start){


A = getrandommatrix(rows, rows, 0, 0, 1);
Dis = getrandommatrix(rows, rows, 0, 0, 1);

for (i = 1; i <= rows-2; i++){
   A[i][i+1] = (A[i][i+1]-0)+1;
}
A[rows-1][1] = (A[rows-1][1]-0)+1;
for(i = 1; i <= rows-1; i++){
  A[i][rows] = (A[i][rows]-0)+1;
} 

for(i = 1; i <= rows; i++){
   for(j = i; j <= rows; j++){
      Dis[i][j] = Math.max((A[i][j]-0),(A[j][i]-0));
      Dis[j][i] = Math.max((A[i][j]-0),(A[j][i]-0));
   }
}


if(double_path_skinnyness == null){double_path_skinnyness = 10};

NRC = MatrixSize(Dis);
var n1 = NRC[0] - 1;
var n = NRC[0];

var fs = getFontSize()/16;
size1 = fs*1200;
size2 = fs*1200;
size3 = fs*(100*fs*fs+410*fs+250);
size4 = fs*(100*fs*fs+410*fs+200);

if(svg_start == null){svg_start = '<iSvg:svg height="'+size1+'" width="'+size2+'" viewBox="0 0 '+size3+' '+size4+'"><iSvg:g id="canvas">';}
    svg_end = '<iSvg:g></iSvg:svg>';

SVG_graph = "";

r = getFontSize()/16*150;
rrloop = getFontSize()/16*50;
rloop = r + rrloop

offset = r+getFontSize()/16*150;
offset2 = r+getFontSize()/16*75;

x_coord = new Array(n);
y_coord = new Array(n);
x_coord_loop = new Array(n);
y_coord_loop = new Array(n);
x_coord_label = new Array(n);
y_coord_label = new Array(n);

for(k = 0; k <= n1-1; k++){
   x_coord[k] = r*Math.cos(2*k*Math.PI/n1)+offset;
   y_coord[k] = r*Math.sin(2*k*Math.PI/n1)+offset;
   x_coord_label[k] = ((1.4*r)+offset2)/2*Math.cos(2*k*Math.PI/n1)+(0.85*offset);
   y_coord_label[k] = ((1.4*r)+offset2)/2*Math.sin(2*k*Math.PI/n1)+(offset);
   x_coord_loop[k] = rloop*Math.cos(2*k*Math.PI/n1)+offset;
   y_coord_loop[k] = rloop*Math.sin(2*k*Math.PI/n1)+offset;
}
   x_coord[n-1] = offset;
   y_coord[n-1] = offset;
   x_coord_label[n-1] = (r/5)+offset;
   y_coord_label[n-1] = (r/5)*Math.sin(2*Math.PI/n1)+offset;
   x_coord_loop[n-1] = offset;
   y_coord_loop[n-1] = offset;

colour = getFgColor();

//SVG_graph += SVG_ellipsebl(x_coord[n-1],y_coord[n-1],0.1,0.1)+SVG_scale_text(x_coord_label[n-1],y_coord_label[n-1],"",colour,fs);

for(i = 1; i <= n; i++) {
   SVG_graph += SVG_ellipsebl(x_coord[i-1],y_coord[i-1],0.1,0.1)+SVG_scale_text(x_coord_label[i-1],y_coord_label[i-1],labels[i-1],colour,fs);

      for(j = 1; j <= n; j++){

         if(A[i][j] == 1){
if(ratio_along_line != 0){SVG_graph += SVG_arrow(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1],ratio_along_line,filled)}else{
SVG_graph += SVG_line(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1])};
      }

   if(A[i][j] == 2){
cxx = (x_coord[i-1]+x_coord[j-1])/2;
cyy = (y_coord[i-1]+y_coord[j-1])/2;
dx = (x_coord[i-1]-x_coord[j-1]);
dy = (y_coord[i-1]-y_coord[j-1]);
if(dx == 0){theta = 90}else{theta = Math.atan(dy/dx)*180/Math.PI};
rxx = Math.pow((x_coord[i-1]-x_coord[j-1])*(x_coord[i-1]-x_coord[j-1])+(y_coord[i-1]-y_coord[j-1])*(y_coord[i-1]-y_coord[j-1]),0.5)/2;
ryy = rxx/double_path_skinnyness; // gives a skinny ellipse
SVG_graph += SVG_ellipse_rotate(cxx,cyy,rxx,ryy,theta,double_path_colour);
      }

   }
// ///////////////// bit for loops on a vertex



         if(A[i][i] != 0){

            SVG_graph += SVG_ellipse(x_coord_loop[i-1],y_coord_loop[i-1],rrloop,rrloop);
      }

// /////////////////



}



return svg_start + SVG_graph + svg_end;
}

//___________________________________________________________________________________________________________________________

function SVG_laddergraph(laddersize,ratio_along_line,filled,svg_start){

double = 2*laddersize;

A = getrandommatrix(double, double, 0, 0, 1);
Dis = getrandommatrix(double, double, 0, 0, 1);

for(i = 1; i <= laddersize - 1; i++){
   A[i][i+1] = 1;
}

for(i = 1; i <= laddersize; i++){
   A[i][i+laddersize] = 1;
}

for(i = laddersize+1; i <= double - 1; i++){
   A[i][i+1] = 1;
}

# alert(A);


for(i = 1; i <= double; i++){
   for(j = i; j <= double; j++){
      Dis[i][j] = Math.max((A[i][j]-0),(A[j][i]-0));
      Dis[j][i] = Math.max((A[i][j]-0),(A[j][i]-0));
   }
}

fs = getFontSize();
size1 = fs/16*1000;
size2 = fs/16*1200;
size3 = fs/16*1200;
size4 = fs/16*1400;

if(svg_start == null){svg_start = '<iSvg:svg height="'+size1+'" width="'+size2+'" viewBox="0 0 '+size3+' '+size4+'"><iSvg:g id="canvas">';}
    svg_end = '<iSvg:g></iSvg:svg>';

SVG_graph = "";

r = getFontSize()/16*150;
offset = r+getFontSize()/16*100;
offset2 = -r+getFontSize()/16*75;
label_shift = getFontSize()/16*5;

x_coord = new Array(n);
y_coord = new Array(n);
x_coord_label = new Array(n);
y_coord_label = new Array(n);

for(k = 0; k <= laddersize-1; k++){
   x_coord[k] = (r*k)-(2*offset2);
   y_coord[k] = offset;
   x_coord_label[k] = x_coord[k];
   y_coord_label[k] = offset-label_shift;
}
for(k = laddersize; k <= double-1; k++){
   x_coord[k] = (r*(k-laddersize))-(2*offset2);
   y_coord[k] = 2*offset;
   x_coord_label[k] = x_coord[k];
   y_coord_label[k] = 2*offset+4*label_shift;
}

colour = getFgColor();
for(i = 1; i <= double; i++) {
   SVG_graph += SVG_ellipsebl(x_coord[i-1],y_coord[i-1],0.1,0.1)+SVG_scale_text(x_coord_label[i-1],y_coord_label[i-1],labels[i],colour,fs/16);

  for(j = 1; j <= double; j++){

         if(A[i][j] == 1){

            if(ratio_along_line != 0){
               SVG_graph += SVG_arrow(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1],ratio_along_line,filled)
            }else{
               SVG_graph += SVG_line(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1])};
            }
         }
   }

return svg_start + SVG_graph + svg_end;
}

//__________________________________________________________________________________________________________________________

//function havel_hakimi_seq(sequence)
//PROBLEM: Works for ONLY 1 iteration, then generates a list of blank lists. WHY???

function havel_hakimi_seq(sequence){

reorder = sorting(sequence,0);
n = reorder.length;

oldlists = new Array();
newlists = new Array();
for(i = 0; i <= n-1; i++){
   oldlists[i] = new Array();
   oldlists[0][i] = (reorder[i]-0);
   newlists[i] = new Array();
   newlists[0][i] = (reorder[i]-0);
}

border = new Array();
pivot = new Array();

for(i = 1; i <= n-1; i++){
   border[i] = newlists[i-1].length - 1;
   oldlists[i] = new Array(border[i]);
   newlists[i] = new Array(border[i]);
   pivot[i] = newlists[i-1][0];
   for(j = 0; j <= (border[i]-0)-1; j++){
      oldlists[i][(border[i]-0)-1-j] = (newlists[i-1][(border[i]-0)-j]-0);
   }
   for(k = 0; k <= (pivot[i]-0)-1; k++){
      oldlists[i][k] = (oldlists[i][k]-0)-1;
   }
   newlists[i] = sorting(oldlists[i],0);
   for(j = 0; j <= (border[i]-0)-1; j++){
      newlists[i][j] = (newlists[i][j]-0);
   }
}

zero = new Array();
for(i = 1; i <= n-1; i++){
   for(j = 0; j <= border[i] - 1; j++){
      if(newlists[i][j] > 0){
         zero[i] += 1;
      }
   }
}

thedisplay = "The original sequence is "+newlists[0]+".<br>";
for(i = 1; i <= n-1; i++){
   if(zero[i] == 0){
      thedisplay += "<br>As there are no more positive integers remaining, the algorithm is terminated.<br>";
   }else{
      thedisplay += "Iteration "+i+" gives "+newlists[i]+".<br>";
   }
}


return(thedisplay);

}
//__________________________________________________________________________________________________________________________

function SVG_shortestpath_network(A,labels,ratio_along_line,filled,double_path_colour,double_path_skinnyness,svg_start){

if(double_path_skinnyness == null){double_path_skinnyness = 10};

NRC = MatrixSize(A);
var n = NRC[0];

var fs = getFontSize()/16;
size1 = fs*800;
size2 = fs*800;
size3 = fs*(100*fs*fs+410*fs+250);
size4 = fs*(100*fs*fs+410*fs+200);

if(svg_start == null){svg_start = '<iSvg:svg height="'+size1+'" width="'+size2+'" viewBox="0 0 '+size3+' '+size4+'"><iSvg:g id="canvas">';}
    svg_end = '<iSvg:g></iSvg:svg>';

SVG_graph = "";

r = getFontSize()/16*200;
rrloop = getFontSize()/16*50;
rloop = r + rrloop

offset = r+getFontSize()/16*200;
offset2 = r+getFontSize()/16*75;

x_coord = new Array(n);
y_coord = new Array(n);
x_coord_loop = new Array(n);
y_coord_loop = new Array(n);
x_coord_label = new Array(n);
y_coord_label = new Array(n);


x_coord[0] = (-1)*r+offset;
y_coord[0] = offset;
x_coord_label[0] = (-1)*((1.4*r)+offset2)/2+(0.9*offset);
y_coord_label[0] = offset;
x_coord_loop[0] = (-1)*rloop+offset;
y_coord_loop[0] = offset;

for(k = 1; k <= n-1; k++){
   x_coord[k] = (-1)*r*Math.cos(2*k*Math.PI/n)+offset;
   y_coord[k] = Math.pow(-1,k)*r*Math.sin(2*k*Math.PI/n)+offset;
   x_coord_label[k] = (-1)*((1.4*r)+offset2)/2*Math.cos(2*k*Math.PI/n)+(0.9*offset);
   y_coord_label[k] = Math.pow(-1,k)*((1.4*r)+offset2)/2*Math.sin(2*k*Math.PI/n)+(offset);
   x_coord_loop[k] = (-1)*rloop*Math.cos(2*k*Math.PI/n)+offset;
   y_coord_loop[k] = Math.pow(-1,k)*rloop*Math.sin(2*k*Math.PI/n)+offset;
}
for(k = 1; k <= n-1; k++){
   if(k%2 == 1){
      x_coord[k] = (-1)*r*Math.cos(2*k*Math.PI/n)+offset;
      y_coord[k] = Math.pow(-1,k)*r*Math.sin(2*k*Math.PI/n)+offset;
      x_coord_label[k] = (-1)*((1.4*r)+offset2)/2*Math.cos(2*k*Math.PI/n)+(0.9*offset);
      y_coord_label[k] = Math.pow(-1,k)*((1.4*r)+offset2)/2*Math.sin(2*k*Math.PI/n)+(offset);
      x_coord_loop[k] = (-1)*rloop*Math.cos(2*k*Math.PI/n)+offset;
      y_coord_loop[k] = Math.pow(-1,k)*rloop*Math.sin(2*k*Math.PI/n)+offset;
   }else{
      x_coord[k] = (-1)*r*Math.cos(2*(k-1)*Math.PI/n)+offset;
      y_coord[k] = Math.pow(-1,k)*r*Math.sin(2*(k-1)*Math.PI/n)+offset;
      x_coord_label[k] = (-1)*((1.4*r)+offset2)/2*Math.cos(2*(k-1)*Math.PI/n)+(0.9*offset);
      y_coord_label[k] = Math.pow(-1,k)*((1.4*r)+offset2)/2*Math.sin(2*(k-1)*Math.PI/n)+(offset);
      x_coord_loop[k] = (-1)*rloop*Math.cos(2*(k-1)*Math.PI/n)+offset;
      y_coord_loop[k] = Math.pow(-1,k)*rloop*Math.sin(2*(k-1)*Math.PI/n)+offset;
   }
}

colour = getFgColor();
for(i = 1; i <= n; i++) {
   SVG_graph += SVG_ellipsebl(x_coord[i-1],y_coord[i-1],0.1,0.1)+SVG_scale_text(x_coord_label[i-1],y_coord_label[i-1],labels[i],colour,fs);

      for(j = 1; j <= n; j++){

         if(A[i][j] == 1){
if(ratio_along_line != 0){SVG_graph += SVG_arrow(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1],ratio_along_line,filled)}else{
SVG_graph += SVG_line(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1])};
      }

   if(A[i][j] == 2){
cxx = (x_coord[i-1]+x_coord[j-1])/2;
cyy = (y_coord[i-1]+y_coord[j-1])/2;
dx = (x_coord[i-1]-x_coord[j-1]);
dy = (y_coord[i-1]-y_coord[j-1]);
if(dx == 0){theta = 90}else{theta = Math.atan(dy/dx)*180/Math.PI};
rxx = Math.pow((x_coord[i-1]-x_coord[j-1])*(x_coord[i-1]-x_coord[j-1])+(y_coord[i-1]-y_coord[j-1])*(y_coord[i-1]-y_coord[j-1]),0.5)/2;
ryy = rxx/double_path_skinnyness; // gives a skinny ellipse
SVG_graph += SVG_ellipse_rotate(cxx,cyy,rxx,ryy,theta,double_path_colour);
      }

   }
// ///////////////// bit for loops on a vertex



         if(A[i][i] != 0){

            SVG_graph += SVG_ellipse(x_coord_loop[i-1],y_coord_loop[i-1],rrloop,rrloop);
      }

// /////////////////



}



return svg_start + SVG_graph + svg_end;
}

//____________________________________________________________________________________


//function SVG_shortest_path(A,labels,ratio_along_line,filled,double_path_colour,vertex_colours,numeric_order,double_path_skinnyness,vertex_radius,svg_start)
//If labels == 0, then alphabetical order is given to the labels.
//If you want large, coloured vertices to appear, then set vertex_radius = 10. Otheriwse, set vertex_radius = 0.1.
//If numeric_order == 0, then normal increasing ordering occurs; otherwise, an array is required for numeric_order.

function SVG_shortest_path(A,labels,ratio_along_line,filled,double_path_colour,vertex_colours,numeric_order,double_path_skinnyness,vertex_radius,svg_start){

if(double_path_skinnyness == null){double_path_skinnyness = 10};

NRC = MatrixSize(A);
var n = NRC[0];

substituted_labels = new Array();
if(labels == 0){
   for(i = 1; i <= n; i++){
      substituted_labels[i] = alphabet(i-1,1);
   }
}else{
   for(i = 1; i <= n; i++){
      substituted_labels[i] = labels[i];
   }
}

var fs = getFontSize()/16;
size1 = fs*800;
size2 = fs*800;
size3 = fs*(100*fs*fs+410*fs+250);
size4 = fs*(100*fs*fs+410*fs+200);

if(svg_start == null){svg_start = '<iSvg:svg height="'+size1+'" width="'+size2+'" viewBox="0 0 '+size3+' '+size4+'"><iSvg:g id="canvas">';}
    svg_end = '<iSvg:g></iSvg:svg>';

SVG_graph = "";

r = getFontSize()/16*150;
rrloop = getFontSize()/16*50;
rloop = r + rrloop;

offset = r+getFontSize()/16*200;
offset2 = r+getFontSize()/16*75;

x_coord = new Array(n);
y_coord = new Array(n);
x_coord_loop = new Array(n);
y_coord_loop = new Array(n);
x_coord_label = new Array(n);
y_coord_label = new Array(n);

for(k = 0; k <= n-1; k++){
   x_coord[k] = (-1)*r*Math.cos(2*Math.ceil(k/2)*Math.PI/n)+offset;
   y_coord[k] = Math.pow(-1,k)*r*Math.sin(2*Math.ceil(k/2)*Math.PI/n)+offset;
   x_coord_label[k] = (-1)*((1.3*r)+offset2)/2*Math.cos(2*Math.ceil(k/2)*Math.PI/n)+(0.98*offset);
   y_coord_label[k] = Math.pow(-1,k)*((1.3*r)+offset2)/2*Math.sin(2*Math.ceil(k/2)*Math.PI/n)+(offset);
   x_coord_loop[k] = (-1)*rloop*Math.cos(2*Math.ceil(k/2)*Math.PI/n)+offset;
   y_coord_loop[k] = Math.pow(-1,k)*rloop*Math.sin(2*Math.ceil(k/2)*Math.PI/n)+offset;
}

colour = getFgColor();

for(i = 1; i <= n; i++) {
   if(numeric_order == 0){
      SVG_graph += SVG_ellipseblx(x_coord[i-1],y_coord[i-1],vertex_radius,vertex_radius,vertex_colours[i-1])+SVG_scale_text(x_coord_label[i-1],y_coord_label[i-1],substituted_labels[i],colour,fs);
   }else{
      SVG_graph += SVG_ellipseblx(x_coord[i-1],y_coord[i-1],vertex_radius,vertex_radius,vertex_colours[(numeric_order[i-1]-0)-1])+SVG_scale_text(x_coord_label[i-1],y_coord_label[i-1],substituted_labels[i],colour,fs);
   }
      for(j = 1; j <= n; j++){

         if(A[i][j] == 1){
if(ratio_along_line != 0){SVG_graph += SVG_arrow(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1],ratio_along_line,filled)}else{
SVG_graph += SVG_line(x_coord[i-1],y_coord[i-1],x_coord[j-1],y_coord[j-1])};
      }

   if(A[i][j] == 2){
cxx = (x_coord[i-1]+x_coord[j-1])/2;
cyy = (y_coord[i-1]+y_coord[j-1])/2;
dx = (x_coord[i-1]-x_coord[j-1]);
dy = (y_coord[i-1]-y_coord[j-1]);
if(dx == 0){theta = 90}else{theta = Math.atan(dy/dx)*180/Math.PI};
rxx = Math.pow((x_coord[i-1]-x_coord[j-1])*(x_coord[i-1]-x_coord[j-1])+(y_coord[i-1]-y_coord[j-1])*(y_coord[i-1]-y_coord[j-1]),0.5)/2;
ryy = rxx/double_path_skinnyness; // gives a skinny ellipse
SVG_graph += SVG_ellipse_rotate(cxx,cyy,rxx,ryy,theta,double_path_colour);
      }
   }
// ///////////////// bit for loops on a vertex



         if(A[i][i] != 0){

            SVG_graph += SVG_ellipse(x_coord_loop[i-1],y_coord_loop[i-1],rrloop,rrloop);
      }






// /////////////////



}


return svg_start + SVG_graph + svg_end;
}

//____________________________________________________________________________________

</script>