funnyKnightMoves.js

//Add this to the browser console of https://www.funnyhowtheknightmoves.com/

/**
 * Creates line element on given position, with given length and angle.
 */
function createLineElement(x, y, length, angle) {
    var line = document.createElement("div");
    var styles = 'border: 1px solid black; '
               + 'width: ' + length + 'px; '
               + 'height: 0px; '
               + '-moz-transform: rotate(' + angle + 'rad); '
               + '-webkit-transform: rotate(' + angle + 'rad); '
               + '-o-transform: rotate(' + angle + 'rad); '
               + '-ms-transform: rotate(' + angle + 'rad); '
               + 'position: absolute; '
               + 'top: ' + y + 'px; '
               + 'left: ' + x + 'px; ';
    line.setAttribute('style', styles);
    return line;
}

function createCircleDiv(x,y,r)
{
 var dot = document.createElement("div");
 var styles = "height: " + 2*r +"px;" 
 	      + "width: " + 2*r +"px;"
 	      + "background-color:#00ff00;"
 	      + "border-radius:50%;"
 	      + "position: absolute;"
 	      + "top: " + (y -r) + "px;"
 	      + "left: " + (x - r) + "px;";
 dot.setAttribute("style",styles);
 return dot;
}

/**
 * Creates element which represents line from point [x1, y1] to [x2, y2].
 * It is html div element with minimal height and width corresponding to line length.
 * It's position and rotation is calculated below.
 */
function createLine(x1, y1, x2, y2) {
    var a = x1 - x2,
        b = y1 - y2,
        c = Math.sqrt(a * a + b * b);

    var sx = (x1 + x2) / 2,
        sy = (y1 + y2) / 2;

    var x = sx - c / 2,
        y = sy;

    var alpha = Math.PI - Math.atan2(-b, a);

    return createLineElement(x, y, c, alpha);
}

// Draw some lines


function getBoardCase(id)
{
  let board = document.querySelector('div.m-auto');
  return board.querySelector('[data-squareid="'+id+'"]');
}

function getBoardCaseCenterCoord(id)
{
  let bcase = getBoardCase(id).getBoundingClientRect();
  return [bcase.left+bcase.width/2,bcase.top+bcase.height/2]
}

function drawLineBetweenBoardCases(id1, id2)
{
let xy1 = getBoardCaseCenterCoord(id1);
let xy2 = getBoardCaseCenterCoord(id2);

document.body.appendChild(createLine(xy1[0], xy1[1], xy2[0], xy2[1]));
}

let forbidden = ["d8", "d7", "d6","d5","d4", "d3", "d2", "d1", "e6", "f7", "g8", "c6", "b7", "a8", "c5", "b5", "a5", "e5", "f5", "g5", "h5", "c4", "b3", "a2", "e4", "f3", "g2", "h1"];


function buildAllGraph()
{
  let letters = ["a","b","c","d","e","f","g","h"];
  let numbers = ["1","2","3","4","5","6","7","8"];
  
  let knightoffset = [[2,1],[1,2],[-1,-2],[-2,-1],[-1,2],[2,-1],[-2,1],[1,-2]];
   
  let ids = [];
  for( i = 0 ; i < 8 ; i++)
  {
  for( j = 0 ; j < 8 ; j++)
  {
    id = letters[i]+numbers[j];
    if( forbidden.includes(id ) ) continue;
    for( k = 0 ; k < knightoffset.length ; k++)
    {
      nx = i+knightoffset[k][0];
      ny = j+knightoffset[k][1];
      if( nx < 0 || ny < 0 || nx > 7 || ny > 7) continue;
      nid = letters[nx]+numbers[ny];
      if( forbidden.includes(nid ) ) continue;
      ids.push([id,nid]);
    } 	
   }
  }

  return ids;
}

//Making the forbidden cases red
((sq) => { let board = document.querySelector('div.m-auto'); sq.forEach(s => board.querySelector('[data-squareid="'+s+'"]').style.backgroundColor='red'); })(forbidden)

var lines  =buildAllGraph();

//Display nodes
for( i = 0 ; i < lines.length ; i++)
{
coord = getBoardCaseCenterCoord( lines[i][0] );
document.body.appendChild(createCircleDiv(coord[0],coord[1],10) );
}

//Display edges
for( i = 0 ; i < lines.length ; i++)
{
 drawLineBetweenBoardCases(lines[i][0],lines[i][1]); 
}

Additional interesting visualization found in the comments :
https://news.ycombinator.com/item?id=34462822 :

https://news.ycombinator.com/item?id=34464240 :