This example will load and display a GEXF encoded graph. Then, when the users rolls the mouse over a node, it will make each edge grey, except the ones that are linked to the node.

function init() {
  // Instanciate sigma.js and customize rendering :
  var sigInst = sigma.init(document.getElementById('sigma-example')).drawingProperties({
    defaultLabelColor: '#fff',
    defaultLabelSize: 14,
    defaultLabelBGColor: '#fff',
    defaultLabelHoverColor: '#000',
    labelThreshold: 6,
    defaultEdgeType: 'curve',
	borderSize: 1,//Something other than 0
    nodeBorderColor: "default",//exactly like this
    defaultNodeBorderColor: "#000",//Any color of your choice
    defaultBorderView: "always"//apply the default color to all nodes always (normal+hover)    
  }).graphProperties({
    minNodeSize: 0.5,
    maxNodeSize: 5,
    minEdgeSize: 1,
    maxEdgeSize: 1
  }).mouseProperties({
    maxRatio: 4
  });

  // Parse a GEXF encoded file to fill the graph
  // (requires "sigma.parseGexf.js" to be included)
  sigInst.parseGexf('les_miserables.gexf');

  // Bind events :
  var greyColor = '#666';
  sigInst.bind('overnodes',function(event){
    var nodes = event.content;
    var neighbors = {};
    sigInst.iterEdges(function(e){
      if(nodes.indexOf(e.source)<0 && nodes.indexOf(e.target)<0){
        if(!e.attr['grey']){
          e.attr['true_color'] = e.color;
          e.color = greyColor;
          e.attr['grey'] = 1;
        }
      }else{
        e.color = e.attr['grey'] ? e.attr['true_color'] : e.color;
        e.attr['grey'] = 0;

        neighbors[e.source] = 1;
        neighbors[e.target] = 1;
      }
    }).iterNodes(function(n){
      if(!neighbors[n.id]){
        if(!n.attr['grey']){
          n.attr['true_color'] = n.color;
          n.color = greyColor;
          n.attr['grey'] = 1;
        }
      }else{
        n.color = n.attr['grey'] ? n.attr['true_color'] : n.color;
        n.attr['grey'] = 0;
      }
    }).draw(2,2,2);
  }).bind('outnodes',function(){
    sigInst.iterEdges(function(e){
      e.color = e.attr['grey'] ? e.attr['true_color'] : e.color;
      e.attr['grey'] = 0;
    }).iterNodes(function(n){
      n.color = n.attr['grey'] ? n.attr['true_color'] : n.color;
      n.attr['grey'] = 0;
    }).draw(2,2,2);
  });

  // Draw the graph :
  sigInst.draw();
}

if (document.addEventListener) {
  document.addEventListener("DOMContentLoaded", init, false);
} else {
  window.onload = init;
}