cluster rendering. Cluster hubs, refactoring

11 years ago · 1f697cfde9
--- a/dist/vis.css
+++ b/dist/vis.css
@ -0,0 +1,235 @@
 .vis.timeline {
 }


 .vis.timeline.rootpanel {
  position: relative;
  overflow: hidden;

  border: 1px solid #bfbfbf;
  -moz-box-sizing: border-box;
  box-sizing: border-box;
 }

 .vis.timeline .panel {
  position: absolute;
  overflow: hidden;
 }


 .vis.timeline .groupset {
  position: absolute;
  padding: 0;
  margin: 0;
 }

 .vis.timeline .labels {
  position: absolute;
  top: 0;
  left: 0;
  width: 100%;
  height: 100%;

  padding: 0;
  margin: 0;

  border-right: 1px solid #bfbfbf;
  box-sizing: border-box;
  -moz-box-sizing: border-box;
 }

 .vis.timeline .labels .label-set {
  position: absolute;
  top: 0;
  left: 0;
  width: 100%;
  height: 100%;

  overflow: hidden;

  border-top: none;
  border-bottom: 1px solid #bfbfbf;
 }

 .vis.timeline .labels .label-set .label {
  position: absolute;
  left: 0;
  top: 0;
  width: 100%;
  color: #4d4d4d;
 }

 .vis.timeline.top .labels .label-set .label,
 .vis.timeline.top .groupset .itemset-axis {
  border-top: 1px solid #bfbfbf;
  border-bottom: none;
 }

 .vis.timeline.bottom .labels .label-set .label,
 .vis.timeline.bottom .groupset .itemset-axis {
  border-top: none;
  border-bottom: 1px solid #bfbfbf;
 }

 .vis.timeline .labels .label-set .label .inner {
  display: inline-block;
  padding: 5px;
 }


 .vis.timeline .itemset {
  position: absolute;
  padding: 0;
  margin: 0;
  overflow: hidden;
 }

 .vis.timeline .background {
 }

 .vis.timeline .foreground {
 }

 .vis.timeline .itemset-axis {
  position: absolute;
 }


 .vis.timeline .item {
  position: absolute;
  color: #1A1A1A;
  border-color: #97B0F8;
  background-color: #D5DDF6;
  display: inline-block;
 }

 .vis.timeline .item.selected {
  border-color: #FFC200;
  background-color: #FFF785;
  z-index: 999;
 }

 .vis.timeline .item.cluster {
  /* TODO: use another color or pattern? */
  background: #97B0F8 url('img/cluster_bg.png');
  color: white;
 }
 .vis.timeline .item.cluster.point {
  border-color: #D5DDF6;
 }

 .vis.timeline .item.box {
  text-align: center;
  border-style: solid;
  border-width: 1px;
  border-radius: 5px;
  -moz-border-radius: 5px; /* For Firefox 3.6 and older */
 }

 .vis.timeline .item.point {
  background: none;
 }

 .vis.timeline .dot {
  border: 5px solid #97B0F8;
  position: absolute;
  border-radius: 5px;
  -moz-border-radius: 5px;  /* For Firefox 3.6 and older */
 }

 .vis.timeline .item.range {
  overflow: hidden;
  border-style: solid;
  border-width: 1px;
  border-radius: 2px;
  -moz-border-radius: 2px;  /* For Firefox 3.6 and older */
 }

 .vis.timeline .item.rangeoverflow {
  border-style: solid;
  border-width: 1px;
  border-radius: 2px;
  -moz-border-radius: 2px;  /* For Firefox 3.6 and older */
 }

 .vis.timeline .item.range .drag-left, .vis.timeline .item.rangeoverflow .drag-left {
  cursor: w-resize;
  z-index: 1000;
 }

 .vis.timeline .item.range .drag-right, .vis.timeline .item.rangeoverflow .drag-right {
  cursor: e-resize;
  z-index: 1000;
 }

 .vis.timeline .item.range .content, .vis.timeline .item.rangeoverflow .content {
  position: relative;
  display: inline-block;
 }

 .vis.timeline .item.line {
  position: absolute;
  width: 0;
  border-left-width: 1px;
  border-left-style: solid;
 }

 .vis.timeline .item .content {
  margin: 5px;
  white-space: nowrap;
  overflow: hidden;
 }

 .vis.timeline .axis {
  position: relative;
 }

 .vis.timeline .axis .text {
  position: absolute;
  color: #4d4d4d;
  padding: 3px;
  white-space: nowrap;
 }

 .vis.timeline .axis .text.measure {
  position: absolute;
  padding-left: 0;
  padding-right: 0;
  margin-left: 0;
  margin-right: 0;
  visibility: hidden;
 }

 .vis.timeline .axis .grid.vertical {
  position: absolute;
  width: 0;
  border-right: 1px solid;
 }

 .vis.timeline .axis .grid.horizontal {
  position: absolute;
  left: 0;
  width: 100%;
  height: 0;
  border-bottom: 1px solid;
 }

 .vis.timeline .axis .grid.minor {
  border-color: #e5e5e5;
 }

 .vis.timeline .axis .grid.major {
  border-color: #bfbfbf;
 }

 .vis.timeline .currenttime {
  background-color: #FF7F6E;
  width: 2px;
  z-index: 9;
 }
 .vis.timeline .customtime {
  background-color: #6E94FF;
  width: 2px;
  cursor: move;
  z-index: 9;
 }
--- a/dist/vis.js
+++ b/dist/vis.js
--- a/dist/vis.min.js
+++ b/dist/vis.min.js
--- a/examples/graph/02.1_really_random_nodes.html
+++ b/examples/graph/02.1_really_random_nodes.html
@ -0,0 +1,114 @@
 <!doctype html>
 <html>
 <head>
    <title>Graph | Really Random nodes</title>

    <style type="text/css">
        body {
            font: 10pt sans;
        }
        #mygraph {
            width: 600px;
            height: 600px;
            border: 1px solid lightgray;
        }
    </style>

    <script type="text/javascript" src="../../dist/vis.js"></script>

    <script type="text/javascript">
        var nodes = null;
        var edges = null;
        var graph = null;

        function draw() {
            nodes = [];
            edges = [];
            // randomly create some nodes and edges
            var nodeCount = parseInt(document.getElementById('nodeCount').value);

            for (var i = 0; i < nodeCount; i++) {
                nodes.push({
                    id: i,
                    label: String(i)
                });
            }
            for (var i = 0; i < nodeCount; i++) {
                var from = i;
                var to = i;
                to = i;
                while (to == i) {
                    to = Math.floor(Math.random() * (nodeCount+1));
                }
                edges.push({
                    from: from,
                    to: to
                });
            }
            /*
            // Loop:
            for (var i = 0; i < 5; i++) {
                nodes.push({
                    id: i,
                    label: String(i)
                });
            }
            edges.push({
                from: 1,
                to: 0
            });
            edges.push({
                from: 1,
                to: 2
            });
            edges.push({
                from: 4,
                to: 0
            });
            edges.push({
                from: 2,
                to: 3
            });
            edges.push({
                from: 3,
                to: 4
            });
            */

            // create a graph
            var container = document.getElementById('mygraph');
            var data = {
                nodes: nodes,
                edges: edges
            };
            var options = {
                edges: {
                    length: 80
                },
                stabilize: false
            };
            graph = new vis.Graph(container, data, options);

            // add event listeners
            vis.events.addListener(graph, 'select', function(params) {
                document.getElementById('selection').innerHTML =
                        'Selection: ' + graph.getSelection();
            });
        }
    </script>
 </head>

 <body onload="draw();">

 <form onsubmit="draw(); return false;">
    <label for="nodeCount">Number of nodes:</label>
    <input id="nodeCount" type="text" value="25" style="width: 50px;">
    <input type="submit" value="Go">
 </form>
 <br>

 <div id="mygraph"></div>

 <p id="selection"></p>
 </body>
 </html>
--- a/src/graph/Edge.js
+++ b/src/graph/Edge.js
@ -269,10 +269,10 @@ Edge.prototype._drawLine = function(ctx) {
 */
 Edge.prototype._getLineWidth = function() {
  if (this.from.selected || this.to.selected) {
    return Math.min(this.width * 2, this.widthMax);
    return Math.min(this.width * 2, this.widthMax)*this.graphScaleInv;
  }
  else {
    return this.width;
    return this.width*this.graphScaleInv;
  }
 };

@ -607,3 +607,14 @@ Edge._dist = function (x1,y1, x2,y2, x3,y3) { // x3,y3 is the point

  return Math.sqrt(dx*dx + dy*dy);
 };



 /**
 * This allows the zoom level of the graph to influence the rendering
 *
 * @param scale
 */
 Edge.prototype.setScale = function(scale) {
  this.graphScaleInv = 1.0/scale;
 };
--- a/src/graph/Graph.js
+++ b/src/graph/Graph.js
@ -39,14 +39,6 @@ function Graph (container, data, options) {
        highlight: {
          border: '#2B7CE9',
          background: '#D2E5FF'
        },
        cluster: {
          border: '#256a2d',
          background: '#2cd140',
          highlight: {
            border: '#899539',
            background: '#c5dc29'
          }
        }
      },
      borderColor: '#2B7CE9',
@ -74,10 +66,11 @@ function Graph (container, data, options) {
      clustering: { // TODO: naming of variables
      maxNumberOfNodes: 100,        // for automatic (initial) clustering //
      clusterLength: 30,            // threshold edge length for clusteringl
      fontSizeMultiplier: 2,        // how much the cluster font size grows per node (in px)
      forceAmplification: 0.6,      // amount of clusterSize between two nodes multiply this value (+1) with the repulsion force
      distanceAmplification: 0.1,   // amount of clusterSize between two nodes multiply this value (+1) with the repulsion force
      edgeGrowth: 10,               // amount of clusterSize connected to the edge is multiplied with this and added to edgeLength
      fontSizeMultiplier: 3,        // how much the cluster font size grows per node (in px)
      forceAmplification: 0.7,      // amount of clusterSize between two nodes multiply this value (+1) with the repulsion force
      distanceAmplification: 0.3,   // amount of clusterSize between two nodes multiply this value (+1) with the repulsion force
      edgeStrength: 0.01,
      edgeGrowth: 11,               // amount of clusterSize connected to the edge is multiplied with this and added to edgeLength
      clusterSizeWidthFactor: 10,
      clusterSizeHeightFactor: 10,
      clusterSizeRadiusFactor: 10,
@ -195,13 +188,12 @@ Graph.prototype.clusterToFit = function() {
  while (numberOfNodes >= maxNumberOfNodes && level < maxLevels) {
    if (level % 5 == 0) {
      console.log("Aggregating Hubs @ level: ",level,". Threshold:", this.hubThreshold,"clusterSession",this.clusterSession);
      this.aggregateHubs();
      this.forceAggregateHubs();
    }
    else {
      console.log("Pulling in Outliers @ level: ",level,"clusterSession",this.clusterSession);
      this.increaseClusterLevel();
    }
    console.log("zoomscale for level: ",this.scale * Math.pow(1.0/11.0,this.clusterSession),". Current: ",this.scale);
    numberOfNodes = this.nodeIndices.length;
    level += 1;
  }
@ -340,7 +332,6 @@ Graph.prototype.setOptions = function (options) {
       if (options.nodes.widthMax) this.constants.nodes.radiusMax = options.nodes.widthMax;
       */
    }

    if (options.groups) {
      for (var groupname in options.groups) {
        if (options.groups.hasOwnProperty(groupname)) {
@ -419,7 +410,7 @@ Graph.prototype._create = function () {
  this.mouseTrap.bind("=",this.decreaseClusterLevel.bind(me));
  this.mouseTrap.bind("-",this.increaseClusterLevel.bind(me));
  this.mouseTrap.bind("s",this.singleStep.bind(me));
  this.mouseTrap.bind("h",this.aggregateHubs.bind(me));
  this.mouseTrap.bind("h",this.forceAggregateHubs.bind(me));
  this.mouseTrap.bind("f",this.toggleFreeze.bind(me));

  // add the frame to the container element
@ -683,10 +674,11 @@ Graph.prototype._zoom = function(scale, pointer) {
 // this.zoomCenter = {"x" : pointer.x,"y" : pointer.y };
  this._setScale(scale);
  this._setTranslation(tx, ty);
  this._updateClusters();
  this.updateClusters();
  this._redraw();

  console.log("current scale: ", this.scale)
  console.log("current zoomscale:",this.scale)

  return scale;
 };

@ -1581,6 +1573,7 @@ Graph.prototype._drawNodes = function(ctx) {
  var selected = [];
  for (var id in nodes) {
    if (nodes.hasOwnProperty(id)) {
      nodes[id].setScale(this.scale);
      if (nodes[id].isSelected()) {
        selected.push(id);
      }
@ -1607,6 +1600,7 @@ Graph.prototype._drawEdges = function(ctx) {
  for (var id in edges) {
    if (edges.hasOwnProperty(id)) {
      var edge = edges[id];
      edge.setScale(this.scale);
      if (edge.connected) {
        edges[id].draw(ctx);
      }
@ -1649,162 +1643,168 @@ Graph.prototype._calculateForces = function() {
      nodes = this.nodes,
      edges = this.edges;

  // gravity, add a small constant force to pull the nodes towards the center of
  // the graph
  // Also, the forces are reset to zero in this loop by using _setForce instead
  // of _addForce

  if (this.nodeIndices.length == 1) { // stop calculation if there is only one node
    nodes[this.nodeIndices[0]]._setForce(0,0);
  }
  else {
    // Gravity is required to keep separated groups from floating off
    // the forces are reset to zero in this loop by using _setForce instead
    // of _addForce
    var gravity = 0.08;
    for (var i = 0; i < this.nodeIndices.length; i++) {
        var node = nodes[this.nodeIndices[i]];
        dx = -node.x - this.translation.x + this.frame.canvas.clientWidth*0.5;
        dy = -node.y - this.translation.y + this.frame.canvas.clientHeight*0.5;

  var gravity = 0.02;
  for (var i = 0; i < this.nodeIndices.length; i++) {
      var node = nodes[this.nodeIndices[i]];
      /*
      dx = -node.x;
      dy = -node.y;
      angle = Math.atan2(dy, dx);
      fx = Math.cos(angle) * gravity;
      fy = Math.sin(angle) * gravity;
      node._setForce(fx, fy);
      */
      node._setForce(0, 0);
  }

  // repulsing forces between nodes
  var minimumDistance = this.constants.nodes.distance,
      steepness = 10; // higher value gives steeper slope of the force around the given minimumDistance


  // we loop from i over all but the last entree in the array
  // j loops from i+1 to the last. This way we do not double count any of the indices, nor i == j
  for (var i = 0; i < this.nodeIndices.length-1; i++) {
    var node1 = nodes[this.nodeIndices[i]];
    for (var j = i+1; j < this.nodeIndices.length; j++) {
      var node2 = nodes[this.nodeIndices[j]];
      var clusterSize = (node1.clusterSize + node2.clusterSize - 2);
      dx = node2.x - node1.x;
      dy = node2.y - node1.y;
      distance = Math.sqrt(dx * dx + dy * dy);


      // clusters have a larger region of influence
      minimumDistance = (clusterSize == 0) ? this.constants.nodes.distance : (this.constants.nodes.distance * (1 + clusterSize * this.constants.clustering.distanceAmplification));
      if (distance < 2*minimumDistance) { // at 2.0 * the minimum distance, the force is 0.000045
        angle = Math.atan2(dy, dx);
        fx = Math.cos(angle) * gravity;
        fy = Math.sin(angle) * gravity;
        node._setForce(fx, fy);

        if (distance < 0.5*minimumDistance) { // at 0.5 * the minimum distance, the force is 0.993307
          repulsingForce = 1.0;
        }
        else {
          // TODO: correct factor for repulsing force
          //repulsingForce = 2 * Math.exp(-5 * (distance * distance) / (dmin * dmin) ); // TODO: customize the repulsing force
          //repulsingForce = Math.exp(-1 * (distance * distance) / (dmin * dmin) ); // TODO: customize the repulsing force
          repulsingForce = 1 / (1 + Math.exp((distance / minimumDistance - 1) * steepness)); // TODO: customize the repulsing force
        }

        // amplify the repulsion for clusters.
        repulsingForce *= (clusterSize == 0) ? 1 : 1 + clusterSize * this.constants.clustering.forceAmplification;
        node.updateDamping(this.nodeIndices.length);
    }

        fx = Math.cos(angle) * repulsingForce;
        fy = Math.sin(angle) * repulsingForce;
    this._updateLabels();

        node1._addForce(-fx, -fy);
        node2._addForce(fx, fy);
      }
    }
  }
    // repulsing forces between nodes
    var minimumDistance = this.constants.nodes.distance,
        steepness = 10; // higher value gives steeper slope of the force around the given minimumDistance

  // TODO: re-implement repulsion of edges
   for (var n = 0; n < nodes.length; n++) {
   for (var l = 0; l < edges.length; l++) {
   var lx = edges[l].from.x+(edges[l].to.x - edges[l].from.x)/2,
   ly = edges[l].from.y+(edges[l].to.y - edges[l].from.y)/2,

   // calculate normally distributed force
   dx = nodes[n].x - lx,
   dy = nodes[n].y - ly,
   distance = Math.sqrt(dx * dx + dy * dy),
   angle = Math.atan2(dy, dx),
    // we loop from i over all but the last entree in the array
    // j loops from i+1 to the last. This way we do not double count any of the indices, nor i == j
    for (var i = 0; i < this.nodeIndices.length-1; i++) {
      var node1 = nodes[this.nodeIndices[i]];
      for (var j = i+1; j < this.nodeIndices.length; j++) {
        var node2 = nodes[this.nodeIndices[j]];
        var clusterSize = (node1.clusterSize + node2.clusterSize - 2);
        dx = node2.x - node1.x;
        dy = node2.y - node1.y;
        distance = Math.sqrt(dx * dx + dy * dy);


   // TODO: correct factor for repulsing force
   //var repulsingforce = 2 * Math.exp(-5 * (distance * distance) / (dmin * dmin) ); // TODO: customize the repulsing force
   //repulsingforce = Math.exp(-1 * (distance * distance) / (dmin * dmin) ), // TODO: customize the repulsing force
   repulsingforce = 1 / (1 + Math.exp((distance / (minimumDistance / 2) - 1) * steepness)), // TODO: customize the repulsing force
   fx = Math.cos(angle) * repulsingforce,
   fy = Math.sin(angle) * repulsingforce;
   nodes[n]._addForce(fx, fy);
   edges[l].from._addForce(-fx/2,-fy/2);
   edges[l].to._addForce(-fx/2,-fy/2);
   }
   }
        // clusters have a larger region of influence
        minimumDistance = (clusterSize == 0) ? this.constants.nodes.distance : (this.constants.nodes.distance * (1 + clusterSize * this.constants.clustering.distanceAmplification));
        if (distance < 2*minimumDistance) { // at 2.0 * the minimum distance, the force is 0.000045
          angle = Math.atan2(dy, dx);

          if (distance < 0.5*minimumDistance) { // at 0.5 * the minimum distance, the force is 0.993307
            repulsingForce = 1.0;
          }
          else {
            // TODO: correct factor for repulsing force
            //repulsingForce = 2 * Math.exp(-5 * (distance * distance) / (dmin * dmin) ); // TODO: customize the repulsing force
            //repulsingForce = Math.exp(-1 * (distance * distance) / (dmin * dmin) ); // TODO: customize the repulsing force
            repulsingForce = 1 / (1 + Math.exp((distance / minimumDistance - 1) * steepness)); // TODO: customize the repulsing force
          }

  // forces caused by the edges, modelled as springs
  for (id in edges) {
    if (edges.hasOwnProperty(id)) {
      var edge = edges[id];
      if (edge.connected) {
        dx = (edge.to.x - edge.from.x);
        dy = (edge.to.y - edge.from.y);
        //edgeLength = (edge.from.width + edge.from.height + edge.to.width + edge.to.height)/2 || edge.length; // TODO: dmin
        //edgeLength = (edge.from.width + edge.to.width)/2 || edge.length; // TODO: dmin
        //edgeLength = 20 + ((edge.from.width + edge.to.width) || 0) / 2;
        edgeLength = edge.length;
        // this implies that the edges between big clusters are longer
        edgeLength += (edge.to.clusterSize + edge.from.clusterSize - 2) * this.constants.clustering.edgeGrowth;
        length =  Math.sqrt(dx * dx + dy * dy);
        angle = Math.atan2(dy, dx);
          // amplify the repulsion for clusters.
          repulsingForce *= (clusterSize == 0) ? 1 : 1 + clusterSize * this.constants.clustering.forceAmplification;

        springForce = edge.stiffness * (edgeLength - length);
          fx = Math.cos(angle) * repulsingForce;
          fy = Math.sin(angle) * repulsingForce;

        fx = Math.cos(angle) * springForce;
        fy = Math.sin(angle) * springForce;
          node1._addForce(-fx, -fy);
          node2._addForce(fx, fy);
        }
      }
    }

        edge.from._addForce(-fx, -fy);
        edge.to._addForce(fx, fy);
    // TODO: re-implement repulsion of edges
     for (var n = 0; n < nodes.length; n++) {
     for (var l = 0; l < edges.length; l++) {
     var lx = edges[l].from.x+(edges[l].to.x - edges[l].from.x)/2,
     ly = edges[l].from.y+(edges[l].to.y - edges[l].from.y)/2,

     // calculate normally distributed force
     dx = nodes[n].x - lx,
     dy = nodes[n].y - ly,
     distance = Math.sqrt(dx * dx + dy * dy),
     angle = Math.atan2(dy, dx),


     // TODO: correct factor for repulsing force
     //var repulsingforce = 2 * Math.exp(-5 * (distance * distance) / (dmin * dmin) ); // TODO: customize the repulsing force
     //repulsingforce = Math.exp(-1 * (distance * distance) / (dmin * dmin) ), // TODO: customize the repulsing force
     repulsingforce = 1 / (1 + Math.exp((distance / (minimumDistance / 2) - 1) * steepness)), // TODO: customize the repulsing force
     fx = Math.cos(angle) * repulsingforce,
     fy = Math.sin(angle) * repulsingforce;
     nodes[n]._addForce(fx, fy);
     edges[l].from._addForce(-fx/2,-fy/2);
     edges[l].to._addForce(-fx/2,-fy/2);
     }
     }


    // forces caused by the edges, modelled as springs
    for (id in edges) {
      if (edges.hasOwnProperty(id)) {
        var edge = edges[id];
        if (edge.connected) {
          var clusterSize = (edge.to.clusterSize + edge.from.clusterSize - 2);
          dx = (edge.to.x - edge.from.x);
          dy = (edge.to.y - edge.from.y);
          //edgeLength = (edge.from.width + edge.from.height + edge.to.width + edge.to.height)/2 || edge.length; // TODO: dmin
          //edgeLength = (edge.from.width + edge.to.width)/2 || edge.length; // TODO: dmin
          //edgeLength = 20 + ((edge.from.width + edge.to.width) || 0) / 2;
          edgeLength = edge.length;
          // this implies that the edges between big clusters are longer
          edgeLength += clusterSize * this.constants.clustering.edgeGrowth;
          length =  Math.sqrt(dx * dx + dy * dy);
          angle = Math.atan2(dy, dx);

          springForce = edge.stiffness * (edgeLength - length);

          // boost strength of cluster springs
          springForce *= (clusterSize == 0) ? 1 : 1 + clusterSize * this.constants.clustering.edgeStrength;

          fx = Math.cos(angle) * springForce;
          fy = Math.sin(angle) * springForce;

          edge.from._addForce(-fx, -fy);
          edge.to._addForce(fx, fy);
        }
      }
    }
  /*
    // TODO: re-implement repulsion of edges

     // repulsing forces between edges
     var minimumDistance = this.constants.edges.distance,
     steepness = 10; // higher value gives steeper slope of the force around the given minimumDistance
     for (var l = 0; l < edges.length; l++) {
     //Keep distance from other edge centers
     for (var l2 = l + 1; l2 < this.edges.length; l2++) {
     //var dmin = (nodes[n].width + nodes[n].height + nodes[n2].width + nodes[n2].height) / 1 || minimumDistance, // TODO: dmin
     //var dmin = (nodes[n].width + nodes[n2].width)/2  || minimumDistance, // TODO: dmin
     //dmin = 40 + ((nodes[n].width/2 + nodes[n2].width/2) || 0),
     var lx = edges[l].from.x+(edges[l].to.x - edges[l].from.x)/2,
     ly = edges[l].from.y+(edges[l].to.y - edges[l].from.y)/2,
     l2x = edges[l2].from.x+(edges[l2].to.x - edges[l2].from.x)/2,
     l2y = edges[l2].from.y+(edges[l2].to.y - edges[l2].from.y)/2,

     // calculate normally distributed force
     dx = l2x - lx,
     dy = l2y - ly,
     distance = Math.sqrt(dx * dx + dy * dy),
     angle = Math.atan2(dy, dx),


     // TODO: correct factor for repulsing force
     //var repulsingforce = 2 * Math.exp(-5 * (distance * distance) / (dmin * dmin) ); // TODO: customize the repulsing force
     //repulsingforce = Math.exp(-1 * (distance * distance) / (dmin * dmin) ), // TODO: customize the repulsing force
     repulsingforce = 1 / (1 + Math.exp((distance / minimumDistance - 1) * steepness)), // TODO: customize the repulsing force
     fx = Math.cos(angle) * repulsingforce,
     fy = Math.sin(angle) * repulsingforce;

     edges[l].from._addForce(-fx, -fy);
     edges[l].to._addForce(-fx, -fy);
     edges[l2].from._addForce(fx, fy);
     edges[l2].to._addForce(fx, fy);
     }
     }
  */
  }
 /*
  // TODO: re-implement repulsion of edges

   // repulsing forces between edges
   var minimumDistance = this.constants.edges.distance,
   steepness = 10; // higher value gives steeper slope of the force around the given minimumDistance
   for (var l = 0; l < edges.length; l++) {
   //Keep distance from other edge centers
   for (var l2 = l + 1; l2 < this.edges.length; l2++) {
   //var dmin = (nodes[n].width + nodes[n].height + nodes[n2].width + nodes[n2].height) / 1 || minimumDistance, // TODO: dmin
   //var dmin = (nodes[n].width + nodes[n2].width)/2  || minimumDistance, // TODO: dmin
   //dmin = 40 + ((nodes[n].width/2 + nodes[n2].width/2) || 0),
   var lx = edges[l].from.x+(edges[l].to.x - edges[l].from.x)/2,
   ly = edges[l].from.y+(edges[l].to.y - edges[l].from.y)/2,
   l2x = edges[l2].from.x+(edges[l2].to.x - edges[l2].from.x)/2,
   l2y = edges[l2].from.y+(edges[l2].to.y - edges[l2].from.y)/2,

   // calculate normally distributed force
   dx = l2x - lx,
   dy = l2y - ly,
   distance = Math.sqrt(dx * dx + dy * dy),
   angle = Math.atan2(dy, dx),


   // TODO: correct factor for repulsing force
   //var repulsingforce = 2 * Math.exp(-5 * (distance * distance) / (dmin * dmin) ); // TODO: customize the repulsing force
   //repulsingforce = Math.exp(-1 * (distance * distance) / (dmin * dmin) ), // TODO: customize the repulsing force
   repulsingforce = 1 / (1 + Math.exp((distance / minimumDistance - 1) * steepness)), // TODO: customize the repulsing force
   fx = Math.cos(angle) * repulsingforce,
   fy = Math.sin(angle) * repulsingforce;

   edges[l].from._addForce(-fx, -fy);
   edges[l].to._addForce(-fx, -fy);
   edges[l2].from._addForce(fx, fy);
   edges[l2].to._addForce(fx, fy);
   }
   }
 */

  this.simulationStep += 1;
 };


--- a/src/graph/Node.js
+++ b/src/graph/Node.js
@ -25,7 +25,6 @@
 function Node(properties, imagelist, grouplist, constants) {
  this.selected = false;


  this.edges = []; // all edges connected to this node
  this.dynamicEdges = [];
  this.reroutedEdges = {};
@ -46,11 +45,13 @@ function Node(properties, imagelist, grouplist, constants) {
  this.xFixed = false;
  this.yFixed = false;
  this.radius = constants.nodes.radius;
  this.baseRadiusValue = constants.nodes.radius;
  this.radiusFixed = false;
  this.radiusMin = constants.nodes.radiusMin;
  this.radiusMax = constants.nodes.radiusMax;

  this.imagelist = imagelist;

  this.grouplist = grouplist;

  this.setProperties(properties, constants);
@ -72,6 +73,8 @@ function Node(properties, imagelist, grouplist, constants) {
  this.vy = 0.0;  // velocity y
  this.minForce = constants.minForce;
  this.damping = 0.9; // damping factor

  this.graphScaleInv = 1;
 }

 /**
@ -93,8 +96,10 @@ Node.prototype.attachEdge = function(edge) {
  if (this.edges.indexOf(edge) == -1) {
    this.edges.push(edge);
  }
  this.dynamicEdges = this.edges;
  this.dynamicEdgesLength = this.edges.length;
  if (this.dynamicEdges.indexOf(edge) == -1) {
    this.dynamicEdges.push(edge);
  }
  this.dynamicEdgesLength = this.dynamicEdges.length;
  this._updateMass();
 };

@ -106,9 +111,9 @@ Node.prototype.detachEdge = function(edge) {
  var index = this.edges.indexOf(edge);
  if (index != -1) {
    this.edges.splice(index, 1);
    this.dynamicEdges.splice(index, 1);
  }
  this.dynamicEdges = this.edges;
  this.dynamicEdgesLength = this.edges.length;
  this.dynamicEdgesLength = this.dynamicEdges.length;
  this._updateMass();
 };

@ -132,13 +137,13 @@ Node.prototype.setProperties = function(properties, constants) {
  }

  // basic properties
  if (properties.id != undefined)        {this.id = properties.id;}
  if (properties.label != undefined)     {this.label = properties.label;}
  if (properties.title != undefined)     {this.title = properties.title;}
  if (properties.group != undefined)     {this.group = properties.group;}
  if (properties.x != undefined)         {this.x = properties.x;}
  if (properties.y != undefined)         {this.y = properties.y;}
  if (properties.value != undefined)     {this.value = properties.value;}
  if (properties.id !== undefined)        {this.id = properties.id;}
  if (properties.label !== undefined)     {this.label = properties.label;}
  if (properties.title !== undefined)     {this.title = properties.title;}
  if (properties.group !== undefined)     {this.group = properties.group;}
  if (properties.x !== undefined)         {this.x = properties.x;}
  if (properties.y !== undefined)         {this.y = properties.y;}
  if (properties.value !== undefined)     {this.value = properties.value;}

  if (this.id === undefined) {
    throw "Node must have an id";
@ -155,17 +160,16 @@ Node.prototype.setProperties = function(properties, constants) {
  }

  // individual shape properties
  if (properties.shape != undefined)          {this.shape = properties.shape;}
  if (properties.image != undefined)          {this.image = properties.image;}
  if (properties.radius != undefined)         {this.radius = properties.radius;}
  if (properties.color != undefined)          {this.color = Node.parseColor(properties.color);}

  if (properties.fontColor != undefined)      {this.fontColor = properties.fontColor;}
  if (properties.fontSize != undefined)       {this.fontSize = properties.fontSize;}
  if (properties.fontFace != undefined)       {this.fontFace = properties.fontFace;}
  if (properties.shape !== undefined)          {this.shape = properties.shape;}
  if (properties.image !== undefined)          {this.image = properties.image;}
  if (properties.radius !== undefined)         {this.radius = properties.radius;}
  if (properties.color !== undefined)          {this.color = Node.parseColor(properties.color);}

  if (properties.fontColor !== undefined)      {this.fontColor = properties.fontColor;}
  if (properties.fontSize !== undefined)       {this.fontSize = properties.fontSize;}
  if (properties.fontFace !== undefined)       {this.fontFace = properties.fontFace;}

  if (this.image != undefined) {
  if (this.image !== undefined) {
    if (this.imagelist) {
      this.imageObj = this.imagelist.load(this.image);
    }
@ -174,9 +178,9 @@ Node.prototype.setProperties = function(properties, constants) {
    }
  }

  this.xFixed = this.xFixed || (properties.x != undefined);
  this.yFixed = this.yFixed || (properties.y != undefined);
  this.radiusFixed = this.radiusFixed || (properties.radius != undefined);
  this.xFixed = this.xFixed || (properties.x !== undefined);
  this.yFixed = this.yFixed || (properties.y !== undefined);
  this.radiusFixed = this.radiusFixed || (properties.radius !== undefined);

  if (this.shape == 'image') {
    this.radiusMin = constants.nodes.widthMin;
@ -219,14 +223,6 @@ Node.parseColor = function(color) {
      highlight: {
        border: color,
        background: color
      },
      cluster: {
        border: color,
        background: color,
        highlight: {
          border: color,
          background: color
        }
      }
    };
    // TODO: automatically generate a nice highlight color
@ -247,33 +243,8 @@ Node.parseColor = function(color) {
      c.highlight.background = color.highlight && color.highlight.background || c.background;
      c.highlight.border = color.highlight && color.highlight.border || c.border;
    }

    // check if cluster colorgroup has been defined
    if (util.isString(color.cluster)) {
      c.cluster = {
        border: color.cluster,
        background: color.cluster
      }
    }
    else {
      c.cluster = {};
      c.cluster.background = color.cluster && color.cluster.background || c.background;
      c.cluster.border = color.cluster && color.cluster.border || c.border;
    }

    // check if cluster highlight colorgroup has been defined
    if (util.isString(color.cluster.highlight)) {
      c.cluster.highlight = {
        border: color.cluster.highlight,
        background: color.cluster.highlight
      }
    }
    else {
      c.cluster.highlight = {};
      c.cluster.highlight.background = color.cluster.highlight && color.cluster.highlight.background || c.background;
      c.cluster.highlight.border = color.cluster.highlight && color.cluster.highlight.border || c.border;
    }
  }

  return c;
 };

@ -537,6 +508,16 @@ Node.prototype._drawImage = function (ctx) {

  var yLabel;
  if (this.imageObj) {
    // draw the shade
    if (this.clusterSize > 1) {
      var lineWidth = ((this.clusterSize > 1) ? 10 : 0.0);
      lineWidth *= this.graphScaleInv;
      lineWidth = Math.min(0.2 * this.width,lineWidth);

      ctx.globalAlpha = 0.5;
      ctx.drawImage(this.imageObj, this.left - lineWidth, this.top - lineWidth, this.width + 2*lineWidth, this.height + 2*lineWidth);
    }
    ctx.globalAlpha = 1.0;
    ctx.drawImage(this.imageObj, this.left, this.top, this.width, this.height);
    yLabel = this.y + this.height / 2;
  }
@ -556,9 +537,9 @@ Node.prototype._resizeBox = function (ctx) {
    this.width = textSize.width + 2 * margin;
    this.height = textSize.height + 2 * margin;

    this.width += this.clusterSize * this.clusterSizeWidthFactor;
    this.height += this.clusterSize * this.clusterSizeHeightFactor;
    this.radius += this.clusterSize * this.clusterSizeRadiusFactor;
    this.width += this.clusterSize * 0.5 * this.clusterSizeWidthFactor;
    this.height += this.clusterSize * 0.5 * this.clusterSizeHeightFactor;
    //this.radius += this.clusterSize * this.clusterSizeRadiusFactor;
  }
 };

@ -568,15 +549,26 @@ Node.prototype._drawBox = function (ctx) {
  this.left = this.x - this.width / 2;
  this.top = this.y - this.height / 2;

  var clusterLineWidth = 2.5;
  var selectionLineWidth = 2;

  ctx.strokeStyle = this.selected ? this.color.highlight.border : this.color.border;

  // draw the outer border
  if (this.clusterSize > 1) {
    ctx.strokeStyle = this.selected ? this.color.cluster.highlight.border : this.color.cluster.border;
    ctx.fillStyle = this.selected ? this.color.cluster.highlight.background : this.color.cluster.background;
  }
  else {
    ctx.strokeStyle = this.selected ? this.color.highlight.border : this.color.border;
    ctx.fillStyle = this.selected ? this.color.highlight.background : this.color.background;
    ctx.lineWidth = (this.selected ? selectionLineWidth : 1.0) + ((this.clusterSize > 1) ? clusterLineWidth : 0.0);
    ctx.lineWidth *= this.graphScaleInv;
    ctx.lineWidth = Math.min(0.1 * this.width,ctx.lineWidth);

    ctx.roundRect(this.left-2*ctx.lineWidth, this.top-2*ctx.lineWidth, this.width+4*ctx.lineWidth, this.height+4*ctx.lineWidth, this.radius);
    ctx.stroke();
  }
  ctx.lineWidth = (this.selected ? 2.0 : 1.0) + (this.clusterSize > 1) ? 2.0 : 0.0;
  ctx.lineWidth = (this.selected ? selectionLineWidth : 1.0) + ((this.clusterSize > 1) ? clusterLineWidth : 0.0);
  ctx.lineWidth *= this.graphScaleInv;
  ctx.lineWidth = Math.min(0.1 * this.width,ctx.lineWidth);

  ctx.fillStyle = this.selected ? this.color.highlight.background : this.color.background;

  ctx.roundRect(this.left, this.top, this.width, this.height, this.radius);
  ctx.fill();
  ctx.stroke();
@ -605,15 +597,25 @@ Node.prototype._drawDatabase = function (ctx) {
  this.left = this.x - this.width / 2;
  this.top = this.y - this.height / 2;

  var clusterLineWidth = 2.5;
  var selectionLineWidth = 2;

  ctx.strokeStyle = this.selected ? this.color.highlight.border : this.color.border;

  // draw the outer border
  if (this.clusterSize > 1) {
    ctx.strokeStyle = this.selected ? this.color.cluster.highlight.border : this.color.cluster.border;
    ctx.fillStyle = this.selected ? this.color.cluster.highlight.background : this.color.cluster.background;
  }
  else {
    ctx.strokeStyle = this.selected ? this.color.highlight.border : this.color.border;
    ctx.fillStyle = this.selected ? this.color.highlight.background : this.color.background;
    ctx.lineWidth = (this.selected ? selectionLineWidth : 1.0) + ((this.clusterSize > 1) ? clusterLineWidth : 0.0);
    ctx.lineWidth *= this.graphScaleInv;
    ctx.lineWidth = Math.min(0.1 * this.width,ctx.lineWidth);

    ctx.database(this.x - this.width/2 - 2*ctx.lineWidth, this.y - this.height*0.5 - 2*ctx.lineWidth, this.width + 4*ctx.lineWidth, this.height + 4*ctx.lineWidth);
    ctx.stroke();
  }
  ctx.lineWidth = (this.selected ? 2.0 : 1.0) + (this.clusterSize > 1) ? 2.0 : 0.0;
  ctx.lineWidth = (this.selected ? selectionLineWidth : 1.0) + ((this.clusterSize > 1) ? clusterLineWidth : 0.0);
  ctx.lineWidth *= this.graphScaleInv;
  ctx.lineWidth = Math.min(0.1 * this.width,ctx.lineWidth);

  ctx.fillStyle = this.selected ? this.color.highlight.background : this.color.background;
  ctx.database(this.x - this.width/2, this.y - this.height*0.5, this.width, this.height);
  ctx.fill();
  ctx.stroke();
@ -635,7 +637,7 @@ Node.prototype._resizeCircle = function (ctx) {
    // scaling used for clustering
    this.width += this.clusterSize * this.clusterSizeWidthFactor;
    this.height += this.clusterSize * this.clusterSizeHeightFactor;
    this.radius += this.clusterSize * this.clusterSizeRadiusFactor;
    this.radius += this.clusterSize * 0.5*this.clusterSizeRadiusFactor;
  }
 };

@ -644,15 +646,25 @@ Node.prototype._drawCircle = function (ctx) {
  this.left = this.x - this.width / 2;
  this.top = this.y - this.height / 2;

  var clusterLineWidth = 2.5;
  var selectionLineWidth = 2;

  ctx.strokeStyle = this.selected ? this.color.highlight.border : this.color.border;

  // draw the outer border
  if (this.clusterSize > 1) {
    ctx.strokeStyle = this.selected ? this.color.cluster.highlight.border : this.color.cluster.border;
    ctx.fillStyle = this.selected ? this.color.cluster.highlight.background : this.color.cluster.background;
  }
  else {
    ctx.strokeStyle = this.selected ? this.color.highlight.border : this.color.border;
    ctx.fillStyle = this.selected ? this.color.highlight.background : this.color.background;
    ctx.lineWidth = (this.selected ? selectionLineWidth : 1.0) + ((this.clusterSize > 1) ? clusterLineWidth : 0.0);
    ctx.lineWidth *= this.graphScaleInv;
    ctx.lineWidth = Math.min(0.1 * this.width,ctx.lineWidth);

    ctx.circle(this.x, this.y, this.radius+2*ctx.lineWidth);
    ctx.stroke();
  }
  ctx.lineWidth = (this.selected ? 2.0 : 1.0) + (this.clusterSize > 1) ? 2.0 : 0.0;
  ctx.lineWidth = (this.selected ? selectionLineWidth : 1.0) + ((this.clusterSize > 1) ? clusterLineWidth : 0.0);
  ctx.lineWidth *= this.graphScaleInv;
  ctx.lineWidth = Math.min(0.1 * this.width,ctx.lineWidth);

  ctx.fillStyle = this.selected ? this.color.highlight.background : this.color.background;
  ctx.circle(this.x, this.y, this.radius);
  ctx.fill();
  ctx.stroke();
@ -682,15 +694,26 @@ Node.prototype._drawEllipse = function (ctx) {
  this.left = this.x - this.width / 2;
  this.top = this.y - this.height / 2;

  var clusterLineWidth = 2.5;
  var selectionLineWidth = 2;

  ctx.strokeStyle = this.selected ? this.color.highlight.border : this.color.border;

  // draw the outer border
  if (this.clusterSize > 1) {
    ctx.strokeStyle = this.selected ? this.color.cluster.highlight.border : this.color.cluster.border;
    ctx.fillStyle = this.selected ? this.color.cluster.highlight.background : this.color.cluster.background;
  }
  else {
    ctx.strokeStyle = this.selected ? this.color.highlight.border : this.color.border;
    ctx.fillStyle = this.selected ? this.color.highlight.background : this.color.background;
    ctx.lineWidth = (this.selected ? selectionLineWidth : 1.0) + ((this.clusterSize > 1) ? clusterLineWidth : 0.0);
    ctx.lineWidth *= this.graphScaleInv;
    ctx.lineWidth = Math.min(0.1 * this.width,ctx.lineWidth);

    ctx.ellipse(this.left-2*ctx.lineWidth, this.top-2*ctx.lineWidth, this.width+4*ctx.lineWidth, this.height+4*ctx.lineWidth);
    ctx.stroke();
  }
  ctx.lineWidth = (this.selected ? 2.0 : 1.0) + (this.clusterSize > 1) ? 2.0 : 0.0;
  ctx.lineWidth = (this.selected ? selectionLineWidth : 1.0) + ((this.clusterSize > 1) ? clusterLineWidth : 0.0);
  ctx.lineWidth *= this.graphScaleInv;
  ctx.lineWidth = Math.min(0.1 * this.width,ctx.lineWidth);

  ctx.fillStyle = this.selected ? this.color.highlight.background : this.color.background;

  ctx.ellipse(this.left, this.top, this.width, this.height);
  ctx.fill();
  ctx.stroke();
@ -719,6 +742,7 @@ Node.prototype._drawStar = function (ctx) {

 Node.prototype._resizeShape = function (ctx) {
  if (!this.width) {
    this.radius = this.baseRadiusValue;
    var size = 2 * this.radius;
    this.width = size;
    this.height = size;
@ -726,7 +750,7 @@ Node.prototype._resizeShape = function (ctx) {
    // scaling used for clustering
    this.width += this.clusterSize * this.clusterSizeWidthFactor;
    this.height += this.clusterSize * this.clusterSizeHeightFactor;
    this.radius += this.clusterSize * this.clusterSizeRadiusFactor;
    this.radius += this.clusterSize * 0.5 * this.clusterSizeRadiusFactor;
  }
 };

@ -735,15 +759,36 @@ Node.prototype._drawShape = function (ctx, shape) {

  this.left = this.x - this.width / 2;
  this.top = this.y - this.height / 2;
  if (this.clusterSize > 1) {
    ctx.strokeStyle = this.selected ? this.color.cluster.highlight.border : this.color.cluster.border;
    ctx.fillStyle = this.selected ? this.color.cluster.highlight.background : this.color.cluster.background;

  var clusterLineWidth = 2.5;
  var selectionLineWidth = 2;
  var radiusMultiplier = 2;

  // choose draw method depending on the shape
  switch (shape) {
    case 'dot':           radiusMultiplier = 2; break;
    case 'square':        radiusMultiplier = 2; break;
    case 'triangle':      radiusMultiplier = 3; break;
    case 'triangleDown':  radiusMultiplier = 3; break;
    case 'star':          radiusMultiplier = 4; break;
  }
  else {
    ctx.strokeStyle = this.selected ? this.color.highlight.border : this.color.border;
    ctx.fillStyle = this.selected ? this.color.highlight.background : this.color.background;

  ctx.strokeStyle = this.selected ? this.color.highlight.border : this.color.border;

  // draw the outer border
  if (this.clusterSize > 1) {
    ctx.lineWidth = (this.selected ? selectionLineWidth : 1.0) + ((this.clusterSize > 1) ? clusterLineWidth : 0.0);
    ctx.lineWidth *= this.graphScaleInv;
    ctx.lineWidth = Math.min(0.1 * this.width,ctx.lineWidth);

    ctx[shape](this.x, this.y, this.radius + radiusMultiplier * ctx.lineWidth);
    ctx.stroke();
  }
  ctx.lineWidth = (this.selected ? 2.0 : 1.0) + (this.clusterSize > 1) ? 2.0 : 0.0;
  ctx.lineWidth = (this.selected ? selectionLineWidth : 1.0) + ((this.clusterSize > 1) ? clusterLineWidth : 0.0);
  ctx.lineWidth *= this.graphScaleInv;
  ctx.lineWidth = Math.min(0.1 * this.width,ctx.lineWidth);

  ctx.fillStyle = this.selected ? this.color.highlight.background : this.color.background;

  ctx[shape](this.x, this.y, this.radius);
  ctx.fill();
@ -798,7 +843,7 @@ Node.prototype._label = function (ctx, text, x, y, align, baseline) {


 Node.prototype.getTextSize = function(ctx) {
  if (this.label != undefined) {
  if (this.label !== undefined) {
    ctx.font = (this.selected ? "bold " : "") + this.fontSize + "px " + this.fontFace;

    var lines = this.label.split('\n'),
@ -815,3 +860,44 @@ Node.prototype.getTextSize = function(ctx) {
    return {"width": 0, "height": 0};
  }
 };

 /**
 * This allows the zoom level of the graph to influence the rendering
 *
 * @param scale
 */
 Node.prototype.setScale = function(scale) {
  this.graphScaleInv = 1.0/scale;
 };

 /**
 * This function updates the damping parameter for clusters, based ont he
 *
 * @param {Integer} numberOfNodes
 */
 Node.prototype.updateDamping = function(numberOfNodes) {
  this.damping = 0.8 + 0.1*this.clusterSize * (1 + 2/Math.pow(numberOfNodes,2));
 };


 /**
 * set the velocity at 0. Is called when this node is contained in another during clustering
 */
 Node.prototype.clearVelocity = function() {
  this.vx = 0;
  this.vy = 0;
 };



 /**
 * Basic preservation of (kinectic) energy
 *
 * @param massBeforeClustering
 */
 Node.prototype.updateVelocity = function(massBeforeClustering) {
  var energyBefore = this.vx * this.vx * massBeforeClustering;
  this.vx = Math.sqrt(energyBefore/this.mass);
  energyBefore = this.vy * this.vy * massBeforeClustering;
  this.vy = Math.sqrt(energyBefore/this.mass);
 };
--- a/src/graph/cluster.js
+++ b/src/graph/cluster.js
@ -7,6 +7,30 @@ function Cluster() {
  this.hubThreshold = 5;
 }


 /**
 * This function can be called to open up a specific cluster.
 * It will unpack the cluster back one level.
 *
 * @param node    | Node object: cluster to open.
 */
 Cluster.prototype.openCluster = function(node) {
  var isMovingBeforeClustering = this.moving;

  this._expandClusterNode(node,false,true);

  // housekeeping
  this._updateNodeIndexList();

  // if the simulation was settled, we restart the simulation if a cluster has been formed or expanded
  if (this.moving != isMovingBeforeClustering) {
    this.start();
  }
 };




 /**
 * This function can be called to increase the cluster level. This means that the nodes with only one edge connection will
 * be clustered with their connected node. This can be repeated as many times as needed.
@ -14,17 +38,30 @@ function Cluster() {
 */
 Cluster.prototype.increaseClusterLevel = function() {
  var isMovingBeforeClustering = this.moving;
  var amountOfNodes = this.nodeIndices.length;

  this._formClusters(true);

  // housekeeping
  this._updateNodeIndexList();
  this._updateDynamicEdges();
  this._updateLabels();

  // if a cluster was formed, we increase the clusterSession
  if (this.nodeIndices.length != amountOfNodes) {
    this.clusterSession += 1;
  }

  // if the simulation was settled, we restart the simulation if a cluster has been formed or expanded
  if (this.moving != isMovingBeforeClustering) {
    this.start();
  }

  this._updateLabels();

 };



 /**
 * This function can be called to decrease the cluster level. This means that the nodes with only one edge connection will
 * be unpacked if they are a cluster. This can be repeated as many times as needed.
@ -39,31 +76,38 @@ Cluster.prototype.decreaseClusterLevel = function() {
      this._expandClusterNode(node,true,true);
    }
  }

  // housekeeping - the dynamic edges are already updated in the expandClusterNode->expelChildFromParent function
  this._updateNodeIndexList();
  this._updateLabels();

  this.clusterSession = (this.clusterSession == 0) ? 0 : this.clusterSession - 1;
  // reduce the clusterSession one level if not at 0
  if (this.clusterSession != 0) {
    this.clusterSession -= 1;
  }

  // if the simulation was settled, we restart the simulation if a cluster has been formed or expanded
  if (this.moving != isMovingBeforeClustering) {
    this.start();
  }

  this._updateLabels();
  console.log("clusterSession",this.clusterSession)
 };


 /**
 * This function can be called to open up a specific cluster.
 * It will unpack the cluster back one level.
 *
 * @param node    | Node object: cluster to open.
 */
 Cluster.prototype.openCluster = function(node) {
 Cluster.prototype.forceAggregateHubs = function() {
  var isMovingBeforeClustering = this.moving;
  var amountOfNodes = this.nodeIndices.length;

  this._expandClusterNode(node,false,true);
  this._aggregateHubs(true);

  // housekeeping
  this._updateNodeIndexList();
  this._updateDynamicEdges();
  this._updateLabels();

  // if a cluster was formed, we increase the clusterSession
  if (this.nodeIndices.length != amountOfNodes) {
    this.clusterSession += 1;
  }

  // if the simulation was settled, we restart the simulation if a cluster has been formed or expanded
  if (this.moving != isMovingBeforeClustering) {
@ -72,6 +116,8 @@ Cluster.prototype.openCluster = function(node) {
 };




 /**
 * This function checks if the zoom action is in or out.
 * If out, check if we can form clusters, if in, check if we can open clusters.
@ -79,20 +125,32 @@ Cluster.prototype.openCluster = function(node) {
 *
 * @private
 */
 Cluster.prototype._updateClusters = function() {
 Cluster.prototype.updateClusters = function() {
  var isMovingBeforeClustering = this.moving;
  var amountOfNodes = this.nodeIndices.length;

  // check if we zoom in or out
  if (this.previousScale > this.scale) { // zoom out
    this._formClusters(false);
    if (this.clusterSession % 5 == 1) {
      this._aggregateHubs(false);
    }
    else {
      this._formClusters(false);
    }
  }
  else if (this.previousScale < this.scale) { // zoom out
    this._openClusters();
  }
  this.previousScale = this.scale;

  this._updateClusterLabels();
  this._updateNodeLabels();
  this._updateNodeIndexList();
  this._updateDynamicEdges();
  this._updateLabels();
  this.previousScale = this.scale;

  // if a cluster was formed, we increase the clusterSession
  if (this.nodeIndices.length != amountOfNodes) { // this means a clustering operation has taken place
    this.clusterSession += 1;
  }

  // if the simulation was settled, we restart the simulation if a cluster has been formed or expanded
  if (this.moving != isMovingBeforeClustering) {
@ -101,54 +159,15 @@ Cluster.prototype._updateClusters = function() {
 };

 /**
 * This updates the node labels for all nodes (for debugging purposes)
 * @private
 * this functions starts clustering by hubs
 * The minimum hub threshold is set globally
 */
 Cluster.prototype._updateLabels = function() {
  // update node labels
  this._updateClusterLabels();
  this._updateNodeLabels();

   // Debug :
  for (var nodeID in this.nodes) {
    if (this.nodes.hasOwnProperty(nodeID)) {
      var node = this.nodes[nodeID];
 //      node.label = String(node.dynamicEdges.length).concat(":",node.dynamicEdgesLength,":",String(node.clusterSize),":::",String(node.id));
      node.label = String(node.dynamicEdges.length).concat(":",String(node.clusterSize));
    }
  }

 Cluster.prototype._aggregateHubs = function(force) {
  this._getHubSize();
  this._clusterByHub(force);
 };

 /**
 * This updates the node labels for all clusters
 * @private
 */
 Cluster.prototype._updateClusterLabels = function() {
  // update node labels
  for (var nodeID in this.nodes) {
    if (this.nodes.hasOwnProperty(nodeID)) {
      var node = this.nodes[nodeID];
      if (node.clusterSize > 1) {
        node.label = "[".concat(String(node.clusterSize),"]");
      }
    }
  }
 };

 /**
 * This updates the node labels for all nodes that are NOT clusters
 * @private
 */
 Cluster.prototype._updateNodeLabels = function() {
  // update node labels
  for (var nodeID in this.nodes) {
    var node = this.nodes[nodeID];
    if (node.clusterSize == 1) {
      node.label = String(node.id);
    }
  }
 };


 /**
@ -158,21 +177,12 @@ Cluster.prototype._updateNodeLabels = function() {
 * @private
 */
 Cluster.prototype._openClusters = function() {
  var amountOfNodes = this.nodeIndices.length;

  for (var i = 0; i < this.nodeIndices.length; i++) {
    var node = this.nodes[this.nodeIndices[i]];
    this._expandClusterNode(node,true,false);
  }

  this._updateNodeIndexList();

  if (this.nodeIndices.length != amountOfNodes) { // this means a clustering operation has taken place
    this.clusterSession -= 1;
  }
 };


 /**
 * This function checks if a node has to be opened. This is done by checking the zoom level.
 * If the node contains child nodes, this function is recursively called on the child nodes as well.
@ -211,17 +221,6 @@ Cluster.prototype._expandClusterNode = function(parentNode, recursive, forceExpa
  }
 };


 Cluster.prototype._parentNodeInActiveArea = function(node) {
  if (Math.abs(node.x - this.zoomCenter.x) <= this.constants.clustering.activeAreaBoxSize/this.scale &&
      Math.abs(node.y - this.zoomCenter.y) <= this.constants.clustering.activeAreaBoxSize/this.scale) {
    return true;
  }
  else {
    return false;
  }
 };

 /**
 * This function will expel a child_node from a parent_node. This is to de-cluster the node. This function will remove
 * the child node from the parent contained_node object and put it back into the global nodes object.
@ -239,7 +238,6 @@ Cluster.prototype._expelChildFromParent = function(parentNode, containedNodeID,

  // if child node has been added on smaller scale than current, kick out
  if (childNode.formationScale < this.scale || forceExpand == true) {

    // put the child node back in the global nodes object
    this.nodes[containedNodeID] = childNode;

@ -249,6 +247,9 @@ Cluster.prototype._expelChildFromParent = function(parentNode, containedNodeID,
    // reconnect rerouted edges to the childNode
    this._connectEdgeBackToChild(parentNode,childNode);

    // validate all edges in dynamicEdges
    this._validateEdges(parentNode);

    // undo the changes from the clustering operation on the parent node
    parentNode.mass -= this.constants.clustering.massTransferCoefficient * childNode.mass;
    parentNode.fontSize -= this.constants.clustering.fontSizeMultiplier * childNode.clusterSize;
@ -281,26 +282,20 @@ Cluster.prototype._expelChildFromParent = function(parentNode, containedNodeID,

 /**
 * This function checks if any nodes at the end of their trees have edges below a threshold length
 * This function is called only from _updateClusters()
 * This function is called only from updateClusters()
 * forceLevelCollapse ignores the length of the edge and collapses one level
 * This means that a node with only one edge will be clustered with its connected node
 *
 * @private
 * @param force_level_collapse    | Boolean
 * @param {Boolean} force
 */
 Cluster.prototype._formClusters = function(forceLevelCollapse) {
  var amountOfNodes = this.nodeIndices.length;

  if (forceLevelCollapse == false) {
 Cluster.prototype._formClusters = function(force) {
  if (force == false) {
    this._formClustersByZoom();
  }
  else {
    this._forceClustersByZoom();
  }

  if (this.nodeIndices.length != amountOfNodes) { // this means a clustering operation has taken place
    this.clusterSession += 1;
  }
 };

 /**
@ -323,37 +318,35 @@ Cluster.prototype._formClustersByZoom = function() {
  // the clustering favours the node with the larger mass
  for (var i = 0; i < edgesIDarray.length; i++) {
    var edgeID = edgesIDarray[i];
    var edge = this.edges[edgeID];
    if (edge.connected) {
      dx = (edge.to.x - edge.from.x);
      dy = (edge.to.y - edge.from.y);
      length = Math.sqrt(dx * dx + dy * dy);


      if (length < minLength) {
        // first check which node is larger
        var parentNode = edge.from
        var childNode = edge.to
        if (edge.to.mass > edge.from.mass) {
          parentNode = edge.to
          childNode = edge.from
        }
    // this is checked because edges can be deleted from this.edges during this function
    // most likely example, two nodes connected to eachother with a double connection
    if (this.edges.hasOwnProperty(edgeID)) {
      var edge = this.edges[edgeID];
      if (edge.connected) {
        dx = (edge.to.x - edge.from.x);
        dy = (edge.to.y - edge.from.y);
        length = Math.sqrt(dx * dx + dy * dy);


        if (length < minLength) {
          // first check which node is larger
          var parentNode = edge.from
          var childNode = edge.to
          if (edge.to.mass > edge.from.mass) {
            parentNode = edge.to
            childNode = edge.from
          }

        // we allow clustering from outside in
        // if we do not cluster from outside in, we would have to reconnect edges or keep
        // a second set of edges for the clusters.
        // This will also have to be altered in the force calculation and rendering.
        // This method is non-destructive and does not require a second set of data.
        if (childNode.dynamicEdgesLength == 1) {
          this._addToCluster(parentNode,childNode,false);
        }
        else if (parentNode.dynamicEdgesLength == 1) {
          this._addToCluster(childNode,parentNode,false);
          if (childNode.dynamicEdgesLength == 1) {
            this._addToCluster(parentNode,childNode,false);
          }
          else if (parentNode.dynamicEdgesLength == 1) {
            this._addToCluster(childNode,parentNode,false);
          }
        }
      }
    }
  }
  this._updateNodeIndexList();
 };

 /**
@ -364,77 +357,39 @@ Cluster.prototype._formClustersByZoom = function() {
 */
 Cluster.prototype._forceClustersByZoom = function() {
  for (var nodeID = 0; nodeID < this.nodeIndices.length; nodeID++) {
    var childNode = this.nodes[this.nodeIndices[nodeID]];
    if (childNode.dynamicEdgesLength == 1) {
      var edge = childNode.dynamicEdges[0];
      var parentNode = (edge.toId == childNode.id) ? this.nodes[edge.fromId] : this.nodes[edge.toId];
      this._addToCluster(parentNode,childNode,true);
    // another node could have absorbed this child.
    if (this.nodes.hasOwnProperty(this.nodeIndices[nodeID])) {
      var childNode = this.nodes[this.nodeIndices[nodeID]];

      // the edges can be swallowed by another decrease
      if (childNode.dynamicEdgesLength == 1 && childNode.dynamicEdges.length != 0) {
        var edge = childNode.dynamicEdges[0];
        var parentNode = (edge.toId == childNode.id) ? this.nodes[edge.fromId] : this.nodes[edge.toId];

        // group to the largest node
        if (parentNode.mass > childNode.mass) {
          this._addToCluster(parentNode,childNode,true);
        }
        else {
          this._addToCluster(childNode,parentNode,true);
        }
      }
    }
  }

  this._updateNodeIndexList();
  this._updateDynamicEdges();
 };


 /**
 * this functions starts clustering by hubs
 * The minimum hub threshold is set globally
 */
 Cluster.prototype.aggregateHubs = function() {
  var isMovingBeforeClustering = this.moving;
  var amountOfNodes = this.nodeIndices.length;

  this._getHubSize();
  this._forceClustersByHub();

  // if the simulation was settled, we restart the simulation if a cluster has been formed or expanded
  if (this.moving != isMovingBeforeClustering) {
    this.start();
  }

  if (this.nodeIndices.length != amountOfNodes) { // this means a clustering operation has taken place
    this.clusterSession += 1;
  }
 };

 /**
 * We determine how many connections denote an important hub.
 * We take the mean + 2*std as the important hub size. (Assuming a normal distribution of data, ~2.2%)
 *
 * @param {Boolean} force
 * @private
 */
 Cluster.prototype._getHubSize = function() {
  var average = 0;
  var averageSquared = 0;
  var hubCounter = 0;

  for (var i = 0; i < this.nodeIndices.length; i++) {
    var node = this.nodes[this.nodeIndices[i]];
    average += node.dynamicEdgesLength;
    averageSquared += Math.pow(node.dynamicEdgesLength,2);
    hubCounter += 1;
  }
  average = average / hubCounter;
  averageSquared = averageSquared / hubCounter;

  var variance = averageSquared - Math.pow(average,2);

  var standardDeviation = Math.sqrt(variance);

  this.hubThreshold = Math.floor(average + 2*standardDeviation);

  //console.log("average",average,"averageSQ",averageSquared,"var",variance,"std",standardDeviation);
  //console.log("hubThreshold:",this.hubThreshold);
 };
 Cluster.prototype._clusterByHub = function(force) {
  var dx,dy,length;
  var minLength = this.constants.clustering.clusterLength/this.scale;
  var allowCluster = false;

 /**
 *
 * @param hubThresholdOverride
 * @param EqualityOverride
 * @private
 */
 Cluster.prototype._forceClustersByHub = function(hubThresholdOverride,EqualityOverride) {
  // we loop over all nodes in the list
  for (var i = 0; i < this.nodeIndices.length; i++) {
    // we check if it is still available since it can be used by the clustering in this loop
@ -450,78 +405,62 @@ Cluster.prototype._forceClustersByHub = function(hubThresholdOverride,EqualityOv
          edgesIDarray.push(hubNode.dynamicEdges[j].id);
        }

        // we loop over all edges INITIALLY connected to this hub
        for (var j = 0; j < amountOfInitialEdges; j++) {
          var edge = this.edges[edgesIDarray[j]];
          var childNode = this.nodes[(edge.fromId == hubNode.id) ? edge.toId : edge.fromId];

          // we do not want hubs to merge with other hubs.
          if (childNode.dynamicEdges.length < this.hubThreshold) {
            this._addToCluster(hubNode,childNode,true);
        // if the hub clustering is not forces, we check if one of the edges connected
        // to a cluster is small enough based on the constants.clustering.clusterLength
        if (force == false) {
          allowCluster = false;
          for (var j = 0; j < amountOfInitialEdges; j++) {
            var edge = this.edges[edgesIDarray[j]];
            if (edge !== undefined) {
              if (edge.connected) {
                dx = (edge.to.x - edge.from.x);
                dy = (edge.to.y - edge.from.y);
                length = Math.sqrt(dx * dx + dy * dy);

                if (length < minLength) {
                  allowCluster = true;
                  break;
                }
              }
            }
          }
        }
      }
    }
  }
  this._updateNodeIndexList();
  this._updateDynamicEdges();
  this._updateLabels();
 };



 /**
 *
 * @param hubThreshold
 * @private
 */
 Cluster.prototype._forceClustersByHub = function() {
  // we loop over all nodes in the list
  for (var i = 0; i < this.nodeIndices.length; i++) {
    // we check if it is still available since it can be used by the clustering in this loop
    if (this.nodes.hasOwnProperty(this.nodeIndices[i])) {
      var hubNode = this.nodes[this.nodeIndices[i]];
        // start the clustering if allowed
        if ((!force && allowCluster) || force) {
          // we loop over all edges INITIALLY connected to this hub
          for (var j = 0; j < amountOfInitialEdges; j++) {
            var edge = this.edges[edgesIDarray[j]];

      // we decide if the node is a hub
      if (hubNode.dynamicEdgesLength >= this.hubThreshold) {
        // we create a list of edges because the dynamicEdges change over the course of this loop
        var edgesIDarray = []
        var amountOfInitialEdges = hubNode.dynamicEdges.length;
        for (var j = 0; j < amountOfInitialEdges; j++) {
          edgesIDarray.push(hubNode.dynamicEdges[j].id);
        }
            // the edge can be clustered by this function in a previous loop
            if (edge !== undefined) {
              var childNode = this.nodes[(edge.fromId == hubNode.id) ? edge.toId : edge.fromId];

        // we loop over all edges INITIALLY connected to this hub
        for (var j = 0; j < amountOfInitialEdges; j++) {
          var edge = this.edges[edgesIDarray[j]];
          var childNode = this.nodes[(edge.fromId == hubNode.id) ? edge.toId : edge.fromId];

          // we do not want hubs to merge with other hubs.
          if (childNode.dynamicEdges.length < this.hubThreshold) {
            this._addToCluster(hubNode,childNode,true);
              // we do not want hubs to merge with other hubs.
              if (childNode.dynamicEdges.length <= this.hubThreshold) {
                this._addToCluster(hubNode,childNode,force);
              }
            }
          }
        }
        //break;
      }
    }
  }
  this._updateNodeIndexList();
  this._updateDynamicEdges();
  this._updateLabels();
 };




 /**
 * This function adds the child node to the parent node, creating a cluster if it is not already.
 * This function is called only from _updateClusters()
 * This function is called only from updateClusters()
 *
 * @param parent_node           | Node object: this is the node that will house the child node
 * @param child_node            | Node object: this node will be deleted from the global this.nodes and stored in the parent node
 * @param force_level_collapse  | Boolean: true will only update the remainingEdges at the very end of the clustering, ensuring single level collapse
 * @param {Node} parentNode           | this is the node that will house the child node
 * @param {Node} childNode            | this node will be deleted from the global this.nodes and stored in the parent node
 * @param {Boolean} force             | true will only update the remainingEdges at the very end of the clustering, ensuring single level collapse
 * @private
 */
 Cluster.prototype._addToCluster = function(parentNode, childNode, forceLevelCollapse) {
 Cluster.prototype._addToCluster = function(parentNode, childNode, force) {
  // join child node in the parent node
  parentNode.containedNodes[childNode.id] = childNode;

@ -537,29 +476,37 @@ Cluster.prototype._addToCluster = function(parentNode, childNode, forceLevelColl
  }
  childNode.dynamicEdges = [];


  // remove the childNode from the global nodes object
  delete this.nodes[childNode.id];

  var massBefore = parentNode.mass;

  childNode.clusterSession = this.clusterSession;
  parentNode.mass += this.constants.clustering.massTransferCoefficient * childNode.mass;
  parentNode.clusterSize += childNode.clusterSize;
  parentNode.fontSize += this.constants.clustering.fontSizeMultiplier * childNode.clusterSize

  // giving the clusters a dynamic formationScale to ensure not all clusters open up when zoomed
  if (forceLevelCollapse == true) {
    parentNode.formationScale = 1.0 * Math.pow(1 - (1.0/11.0),this.clusterSession + parentNode.clusterSize);
  if (force == true) {
    parentNode.formationScale = 1.0 * Math.pow(1 - (1.0/11.0),this.clusterSession+2);
    console.log(".formationScale",parentNode.formationScale)
  }
  else {
    parentNode.formationScale = this.scale; // The latest child has been added on this scale
  }
  console.log("formationScale",parentNode.formationScale)
  parentNode.dynamicEdgesLength = parentNode.dynamicEdges.length;

  // recalculate the size of the node on the next time the node is rendered
  parentNode.clearSizeCache();

  parentNode.containedNodes[childNode.id].formationScale = this.scale; // this child has been added at this scale.
  // set the pop-out scale for the childnode
  parentNode.containedNodes[childNode.id].formationScale = parentNode.formationScale;

  // nullify the movement velocity of the child, this is to avoid hectic behaviour
  childNode.clearVelocity();

  // the mass has altered, preservation of energy dictates the velocity to be updated
  parentNode.updateVelocity(massBefore);


  // restart the simulation to reorganise all nodes
  this.moving = true;
@ -576,23 +523,27 @@ Cluster.prototype._updateDynamicEdges = function() {
  for (var i = 0; i < this.nodeIndices.length; i++) {
    var node = this.nodes[this.nodeIndices[i]];
    node.dynamicEdgesLength = node.dynamicEdges.length;
  }
 };


 Cluster.prototype._repositionNodes = function() {
  for (var i = 0; i < this.nodeIndices.length; i++) {
    var node = this.nodes[this.nodeIndices[i]];
    if (!node.isFixed()) {
      // TODO: position new nodes in a smarter way!
      var radius = this.constants.edges.length * (1 + 0.5*node.clusterSize);
      var angle = 2 * Math.PI * Math.random();
      node.x = radius * Math.cos(angle);
      node.y = radius * Math.sin(angle);
    // this corrects for multiple edges pointing at the same other node
    var correction = 0
    if (node.dynamicEdgesLength > 1) {
      for (var j = 0; j < node.dynamicEdgesLength - 1; j++) {
        var edgeToId = node.dynamicEdges[j].toId;
        var edgeFromId = node.dynamicEdges[j].fromId;
        for (var k = j+1; k < node.dynamicEdgesLength; k++) {
          if ((node.dynamicEdges[k].toId == edgeToId && node.dynamicEdges[k].fromId == edgeFromId) ||
              (node.dynamicEdges[k].fromId == edgeToId && node.dynamicEdges[k].toId == edgeFromId)) {
            correction += 1;
          }
        }
      }
    }

    node.dynamicEdgesLength -= correction;
  }
 };


 /**
 * This adds an edge from the childNode to the contained edges of the parent node
 *
@ -706,6 +657,27 @@ Cluster.prototype._connectEdgeBackToChild = function(parentNode, childNode) {
  }
 };


 /**
 * When loops are clustered, an edge can be both in the rerouted array and the contained array.
 * This function is called last to verify that all edges in dynamicEdges are in fact connected to the
 * parentNode
 *
 * @param parentNode    | Node object
 * @param childNode     | Node object
 * @private
 */
 Cluster.prototype._validateEdges = function(parentNode) {
  // TODO: check if good idea
  for (var i = 0; i < parentNode.dynamicEdges.length; i++) {
    var edge = parentNode.dynamicEdges[i];
    if (parentNode.id != edge.toId && parentNode.id != edge.fromId) {
      parentNode.dynamicEdges.splice(i,1);
    }
  }
 };


 /**
 * This function released the contained edges back into the global domain and puts them back into the
 * dynamic edges of both parent and child.
@ -729,3 +701,123 @@ Cluster.prototype._releaseContainedEdges = function(parentNode, childNode) {
  delete parentNode.containedEdges[childNode.id];

 };




 // ------------------- UTILITY FUNCTIONS ---------------------------- //


 /**
 * This updates the node labels for all nodes (for debugging purposes)
 * @private
 */
 Cluster.prototype._updateLabels = function() {
  // update node labels
  for (var nodeID in this.nodes) {
    if (this.nodes.hasOwnProperty(nodeID)) {
      var node = this.nodes[nodeID];
      if (node.clusterSize > 1) {
        node.label = "[".concat(String(node.clusterSize),"]");
      }
    }
  }

  // update node labels
  for (var nodeID in this.nodes) {
    var node = this.nodes[nodeID];
    if (node.clusterSize == 1) {
      node.label = String(node.id);
    }
  }

  /* Debug Override */
  for (var nodeID in this.nodes) {
    if (this.nodes.hasOwnProperty(nodeID)) {
      var node = this.nodes[nodeID];
      node.label = String(node.dynamicEdges.length).concat(":",node.dynamicEdgesLength,":",String(node.clusterSize),":::",String(node.id));
    }
  }

 };


 /**
 * This function determines if the cluster we want to decluster is in the active area
 * this means around the zoom center
 *
 * @param {Node}
 * @returns {boolean}
 * @private
 */
 Cluster.prototype._parentNodeInActiveArea = function(node) {
  if (Math.abs(node.x - this.zoomCenter.x) <= this.constants.clustering.activeAreaBoxSize/this.scale &&
    Math.abs(node.y - this.zoomCenter.y) <= this.constants.clustering.activeAreaBoxSize/this.scale) {
    return true;
  }
  else {
    return false;
  }
 };


 /**
 * This is an adaptation of the original repositioning function. This is called if the system is clustered initially
 * It puts large clusters away from the center and randomizes the order.
 *
 * @private
 */
 Cluster.prototype._repositionNodes = function() {
  for (var i = 0; i < this.nodeIndices.length; i++) {
    var node = this.nodes[this.nodeIndices[i]];
    if (!node.isFixed()) {
      var radius = this.constants.edges.length * (1 + 0.6*node.clusterSize);
      var angle = 2 * Math.PI * Math.random();
      node.x = radius * Math.cos(angle);
      node.y = radius * Math.sin(angle);
    }
  }
 };





 /**
 * We determine how many connections denote an important hub.
 * We take the mean + 2*std as the important hub size. (Assuming a normal distribution of data, ~2.2%)
 *
 * @private
 */
 Cluster.prototype._getHubSize = function() {
  var average = 0;
  var averageSquared = 0;
  var hubCounter = 0;
  var largestHub = 0;

  for (var i = 0; i < this.nodeIndices.length; i++) {
    var node = this.nodes[this.nodeIndices[i]];
    if (node.dynamicEdgesLength > largestHub) {
      largestHub = node.dynamicEdgesLength;
    }
    average += node.dynamicEdgesLength;
    averageSquared += Math.pow(node.dynamicEdgesLength,2);
    hubCounter += 1;
  }
  average = average / hubCounter;
  averageSquared = averageSquared / hubCounter;

  var variance = averageSquared - Math.pow(average,2);

  var standardDeviation = Math.sqrt(variance);

  this.hubThreshold = Math.floor(average + 2*standardDeviation);

  // always have at least one to cluster
  if (this.hubThreshold > largestHub) {
    this.hubThreshold = largestHub;
  }

 //  console.log("average",average,"averageSQ",averageSquared,"var",variance,"std",standardDeviation);
 //  console.log("hubThreshold:",this.hubThreshold);
 };
--- a/vis.min.js
+++ b/vis.min.js