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

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license: bsd-3-clause
height: 500

README.md

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.

d3-force-sampled.js

// Copyright 2019 Two Six Labs, LLC. v1.0.0 d3-force-sampled https://github.com/twosixlabs/d3-force-sampled/
(function (global, factory) {
typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports) :
typeof define === 'function' && define.amd ? define(['exports'], factory) :
(factory((global.d3 = global.d3 || {})));
}(this, (function (exports) { 'use strict';

function constant(x) {
  return function() {
    return x;
  };
}

function manyBodySampled() {
  var nodes,
      alpha,
      strength = constant(-30),
      strengths,
      indicesRepulse,
      prevIndex = 0,
      distanceMin2 = 1,
      distanceMax2 = Infinity,
      neighborSize = function () {
        return 15;
      },
      updateSize = function (nodes) { return Math.pow(nodes.length, 0.75); },
      sampleSize = function (nodes) { return Math.pow(nodes.length, 0.25); },
      numNeighbors,
      numUpdate,
      numSamples,
      chargeMultiplier = function (nodes) {
        return nodes.length < 100 ? 1 : nodes.length < 200 ? 3 : Math.sqrt(nodes.length);
      },
      cMult,
      rand = Math.random;

  function addRandomNode(node) {
    var randIdx = Math.floor(rand() * nodes.length),
        randNode = nodes[randIdx],
        randDist = (node.x - randNode.x) * (node.x - randNode.x) + (node.y - randNode.y) * (node.y - randNode.y),
        currIdx,
        currNode,
        currDist,
        maxI,
        maxDist = -Infinity,
        i = -1;

    // Is this already in the list?
    if (node.nearest.indexOf(randIdx) >= 0) return;

    // If there is room for another, add it.
    if (node.nearest.length < numNeighbors) {
      node.nearest.push(randIdx);
      return;
    }

    // Replace the farthest away "neighbor" with the new node.
    while (++i < node.nearest.length) {
      currIdx = node.nearest[i];
      currNode = nodes[currIdx];
      currDist = Math.hypot(node.x - currNode.x, node.y - currNode.y);
      if (currDist > maxDist) {
        maxI = i;
        maxDist = currDist;
      }
    }

    if (randDist < maxDist) {
      node.nearest[maxI] = randIdx;
    }
  }

  function getRandIndices(indices, num) {
    num = Math.floor(num);
    var i,
        n = nodes.length,
        cnt = n - num,
        randIdx,
        temp;

    // Choose random indices.
    for (i = n-1; i >= cnt; --i) {
      randIdx = Math.floor(rand() * i);
      temp = indices[randIdx];
      indices[randIdx] = indices[i];
      indices[i] = temp;
    }

    return indices.slice(cnt);
  }

  function approxRepulse(node) {
    var i,
        randIndices,
        currNode,
        w,
        x,
        y,
        l;

    // Choose random nodes to update.
    randIndices = getRandIndices(indicesRepulse, numSamples);

    for (i = randIndices.length - 1; i >= 0; --i) {
      currNode = nodes[randIndices[i]];

      if (currNode === node) continue;

      x = currNode.x - node.x;
      y = currNode.y - node.y;
      l = x * x + y * y;

      if (l >= distanceMax2) continue;

      // Limit forces for very close nodes; randomize direction if coincident.
      if (x === 0) x = (rand() - 0.5) * 1e-6, l += x * x;
      if (y === 0) y = (rand() - 0.5) * 1e-6, l += y * y;
      if (l < distanceMin2) l = Math.sqrt(distanceMin2 * l);

      w = strengths[node.index] * alpha * cMult / l;
      node.vx += x * w;
      node.vy += y * w;
    }
  }

  function constantRepulse(node) {
    var i,
        nearest,
        currNode,
        w,
        x,
        y,
        l;

    // Update the list of nearest nodes.
    if (numNeighbors) addRandomNode(node);

    nearest = node.nearest;

    if (numNeighbors) for (i = nearest.length - 1; i >= 0; --i) {
      currNode = nodes[nearest[i]];

      if (currNode === node) continue;

      x = currNode.x - node.x;
      y = currNode.y - node.y;
      l = x * x + y * y;

      if (l >= distanceMax2) continue;

      // Limit forces for very close nodes; randomize direction if coincident.
      if (x === 0) x = (rand() - 0.5) * 1e-6, l += x * x;
      if (y === 0) y = (rand() - 0.5) * 1e-6, l += y * y;
      if (l < distanceMin2) l = Math.sqrt(distanceMin2 * l);

      w = strengths[node.index] * alpha * cMult / l;
      node.vx += x * w;
      node.vy += y * w;
    }
  }

  function force(_) {
    var i = 0, j = prevIndex, n = nodes.length, upperIndex = prevIndex + numUpdate;
    for (alpha = _; i < n || j < upperIndex; ++i, ++j) {
      if (j < upperIndex) approxRepulse(nodes[j%n]);
      if (numNeighbors && i < n) constantRepulse(nodes[i]);
    }
    prevIndex = upperIndex % n;
  }

  function initialize() {
    if (!nodes) return;
    var i, n = nodes.length, node;
    indicesRepulse = new Array(n);
    for (i = 0; i < n; ++i) indicesRepulse[i] = i;
    strengths = new Array(n);
    
    // Cannot be negative.
    numNeighbors = Math.min(Math.ceil(neighborSize(nodes)), n);
    numNeighbors = numNeighbors < 0 ? 0 : Math.min(numNeighbors, nodes.length);
    numUpdate = Math.ceil(updateSize(nodes));
    numUpdate = numUpdate < 0 ? 0 : Math.min(numUpdate, n);
    numSamples = Math.ceil(sampleSize(nodes));
    numSamples = numSamples < 0 ? 0 : Math.min(numSamples, n);

    cMult = chargeMultiplier(nodes);

    alpha = 1;
    for (i = 0; i < n; ++i) {
      node = nodes[i];
      strengths[node.index] = +strength(node, i, nodes);
      node.nearest = [];
      while (node.nearest.length < numNeighbors) addRandomNode(node);
    }
  }

  force.initialize = function(_) {
    nodes = _;
    initialize();
  };

  force.strength = function(_) {
    return arguments.length ? (strength = typeof _ === "function" ? _ : constant(+_), initialize(), force) : strength;
  };

  force.distanceMin = function(_) {
    return arguments.length ? (distanceMin2 = _ * _, force) : Math.sqrt(distanceMin2);
  };

  force.distanceMax = function(_) {
    return arguments.length ? (distanceMax2 = _ * _, force) : Math.sqrt(distanceMax2);
  };

  force.neighborSize = function(_) {
    return arguments.length ? (neighborSize = typeof _ === "function" ? _ : constant(+_), initialize(), force) : neighborSize;
  };

  force.updateSize = function(_) {
    return arguments.length ? (updateSize = typeof _ === "function" ? _ : constant(+_), initialize(), force) : updateSize;
  };

  force.sampleSize = function(_) {
    return arguments.length ? (sampleSize = typeof _ === "function" ? _ : constant(+_), initialize(), force) : sampleSize;
  };

  force.chargeMultiplier = function(_) {
    return arguments.length ? (chargeMultiplier = typeof _ === "function" ? _ : constant(+_), initialize(), force) : chargeMultiplier;
  };

  force.source = function(_) {
    return arguments.length ? (rand = _, force) : rand;
  };

  return force;
}

exports.forceManyBodySampled = manyBodySampled;

Object.defineProperty(exports, '__esModule', { value: true });

})));

dwt_1005.json

{"category": "benchmark", "gragnostics": {"bridge": 0.0, "star": 0.018385083792447358, "disconnected": 0.0, "links": 4813, "density": 0.007547917781609879, "isolation": 0.0, "line": 0.0, "constricted": 0.0, "tree": 0.9888931121719606, "nodes": 1005}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}, {"id": 8}, {"id": 9}, {"id": 10}, {"id": 11}, {"id": 12}, {"id": 13}, {"id": 14}, {"id": 15}, {"id": 16}, {"id": 17}, {"id": 18}, {"id": 19}, {"id": 20}, {"id": 21}, {"id": 22}, {"id": 23}, {"id": 24}, {"id": 25}, {"id": 26}, {"id": 27}, {"id": 28}, {"id": 29}, {"id": 30}, {"id": 31}, {"id": 32}, {"id": 33}, {"id": 34}, {"id": 35}, {"id": 36}, {"id": 37}, {"id": 38}, {"id": 39}, {"id": 40}, {"id": 41}, {"id": 42}, {"id": 43}, {"id": 44}, {"id": 45}, {"id": 46}, {"id": 47}, {"id": 48}, {"id": 49}, {"id": 50}, {"id": 51}, {"id": 52}, {"id": 53}, {"id": 54}, {"id": 55}, {"id": 56}, {"id": 57}, {"id": 58}, {"id": 59}, {"id": 60}, {"id": 61}, {"id": 62}, {"id": 63}, {"id": 64}, {"id": 65}, {"id": 66}, {"id": 67}, {"id": 68}, {"id": 69}, {"id": 70}, {"id": 71}, {"id": 72}, {"id": 73}, {"id": 74}, {"id": 75}, {"id": 76}, {"id": 77}, {"id": 78}, {"id": 79}, {"id": 80}, {"id": 81}, {"id": 82}, {"id": 83}, {"id": 84}, {"id": 85}, {"id": 86}, {"id": 87}, {"id": 88}, {"id": 89}, {"id": 90}, {"id": 91}, {"id": 92}, {"id": 93}, {"id": 94}, {"id": 95}, {"id": 96}, {"id": 97}, {"id": 98}, {"id": 99}, {"id": 100}, {"id": 101}, {"id": 102}, {"id": 103}, {"id": 104}, {"id": 105}, {"id": 106}, {"id": 107}, {"id": 108}, {"id": 109}, {"id": 110}, {"id": 111}, {"id": 112}, {"id": 113}, {"id": 114}, {"id": 115}, {"id": 116}, {"id": 117}, {"id": 118}, {"id": 119}, {"id": 120}, {"id": 121}, {"id": 122}, {"id": 123}, {"id": 124}, {"id": 125}, {"id": 126}, {"id": 127}, {"id": 128}, {"id": 129}, {"id": 130}, {"id": 131}, {"id": 132}, {"id": 133}, {"id": 134}, {"id": 135}, {"id": 136}, {"id": 137}, {"id": 138}, {"id": 139}, {"id": 140}, {"id": 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{"source": 988, "target": 992}, {"source": 989, "target": 1004}, {"source": 989, "target": 989}, {"source": 990, "target": 1003}, {"source": 990, "target": 1000}, {"source": 990, "target": 991}, {"source": 990, "target": 990}, {"source": 991, "target": 999}, {"source": 991, "target": 1000}, {"source": 991, "target": 991}, {"source": 991, "target": 992}, {"source": 992, "target": 1004}, {"source": 992, "target": 999}, {"source": 992, "target": 1002}, {"source": 992, "target": 992}, {"source": 993, "target": 993}, {"source": 994, "target": 994}, {"source": 995, "target": 995}, {"source": 995, "target": 996}, {"source": 995, "target": 998}, {"source": 995, "target": 999}, {"source": 995, "target": 1000}, {"source": 996, "target": 996}, {"source": 996, "target": 1000}, {"source": 996, "target": 1001}, {"source": 996, "target": 1003}, {"source": 997, "target": 997}, {"source": 997, "target": 1001}, {"source": 998, "target": 998}, {"source": 998, "target": 999}, {"source": 998, "target": 1002}, {"source": 999, "target": 999}, {"source": 999, "target": 1000}, {"source": 999, "target": 1002}, {"source": 1000, "target": 1000}, {"source": 1000, "target": 1003}, {"source": 1001, "target": 1003}, {"source": 1001, "target": 1001}, {"source": 1002, "target": 1002}, {"source": 1002, "target": 1004}, {"source": 1003, "target": 1003}, {"source": 1004, "target": 1004}]}

index.html

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

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

<canvas width="500" height="500"></canvas>

<script src="https://d3js.org/d3.v5.min.js"></script>
<script src="d3-force-sampled.js"></script>
<script>

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>

preview.png

thumbnail.png