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Linear-time force-directed graph layouts with random vertex sampling
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.block
license: bsd-3-clause
height: 500
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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.

Raw
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 });
})));
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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}]}
Raw
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>
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