Linear-time force-directed graph layouts with random vertex sampling

A simple example showing how to use d3.forceManyBodySampled() from d3-force-sampled for force-directed graph layouts. This example shows the dwt_1005 benchmark graph, which has 1005 vertices and 4813 edges.

d3.forceManyBodySampled() is a fast force calculation replacement for d3.forceManyBody(). It achieves this performance improvement by using Random Vertex Sampling instead of the Barnes-Hut approximation. Instead of computing Coulombic forces on every vertex at every iteration, Random Vertex Sampling only computes forces on a subset of vertices. And for each vertex in that subset, Random Vertex Sampling uses a different random sample of vertices to compute forces. This results in an algorithm that runs in linear time with linear space requirements. See d3-force-sampled and the research paper for more details:

Robert Gove. "A Random Sampling O(n) Force-calculation Algorithm for Graph Layouts." Computer Graphics Forum 38, 3 (2019). Preprint PDF.

<!DOCTYPE html>
<meta charset="utf-8">
<style>
  body {
    font-family: Arial, "Helvetica Neue", Helvetica, sans-serif;
    background: white;
  }

canvas {
    margin: 0 230px;
  }
</style>
<body>

var radius = 1;
var tick = 300;

var canvas = document.querySelector('canvas');
var context = canvas.getContext('2d');

var width = canvas.width;
var height = canvas.height;

var scale = d3.scaleLinear()
  .range([radius, width - radius])
  .domain([-3200, 3200]);

var forceSim = d3.forceSimulation()
  .velocityDecay(0.2)
  .alphaDecay(0)
  .force('link', d3.forceLink())
  .force('charge', d3.forceManyBodySampled())
  .force('center', d3.forceCenter(width/2, height/2));

d3.json('dwt_1005.json').then(function(graph) {
  forceSim.nodes(graph.nodes)
    .on('tick', function () {
      drawNetwork(graph);
      if (--tick < 0) forceSim.stop();
    });

forceSim.force('link')
    .links(graph.links);
});

function drawNetwork (graph) {
  context.clearRect(0, 0, width, height);
  context.fillStyle = '#ffffff';
  context.fillRect(0, 0, width, height);

// Draw links.
  context.strokeStyle = 'rgba(90, 90, 90, 0.30)';
  context.lineWidth = 1;
  graph.links.forEach(function(d) {
    context.beginPath();
    var pos = [scale(d.source.x), scale(d.source.y)];
    context.moveTo(pos[0], pos[1]);
    pos = [scale(d.target.x), scale(d.target.y)];
    context.lineTo(pos[0], pos[1]);
    context.stroke();
  });

// Draw nodes.
  context.fillStyle = '#d30000';
  context.beginPath();
  graph.nodes.forEach(function(d) {
    var pos = [scale(d.x), scale(d.y)];
    context.moveTo(pos[0], pos[1]);
    context.arc(pos[0], pos[1], radius, 0, 2 * Math.PI);
  });
  context.fill();
}

</script>

https://d3js.org/d3.v5.min.js