This module includes d3.forceManyBodySampled(), a faster version of the repulsive force algorithm in d3-force. This module has zero dependencies. In practice, d3.forceManyBodySampled() can compute force-directed graph layouts 2.9 times faster on average than D3's forceManyBody(), which is based on the Barnes–Hut approximation. It can achieve this without a decrease in graph readability metrics for the resulting graph layout.
This module uses the Random Vertex Sampling (RVS) algorithm. The Barnes-Hut approximation and Fast Multipole Method both use a spatial tree to compute approximate forces on each vertex, or node, in the graph. This means they run in O(|V| log(|V|)) time and require O(|V| log(|V|)) space for a graph with |V| vertices. In contrast, RVS runs in O(|V|) time and requires O(|V|^(3/4)) auxiliary space, or O(|V|) space overall. For specifics of the algorithm, see the research paper, or this blog post for a simplified explanation.
For a different approach to speeding up force layouts, see also d3-force-reuse.
If you use this module, please cite the following research paper:
Robert Gove. "A Random Sampling O(n) Force-calculation Algorithm for Graph Layouts." Computer Graphics Forum 38, 3 (2019) pp. 739--751. Preprint PDF.
This module heavily uses code from d3-force. Many thanks to Mike Bostock for making this resource available open source!
If you use NPM, npm install d3-force-sampled. Otherwise, download the latest release. AMD, CommonJS, and vanilla environments are supported.
d3.forceManyBodySampled() extends the d3.forceManyBody() API, and therefore can be used as a drop-in replacement for d3.forceManyBody(). The following is a simple example:
<script src="https://d3js.org/d3.v5.min.js"></script>
<script src="d3-force-sampled.js"></script>
<script>
var simulation = d3.forceSimulation(nodes)
.velocityDecay(0.2)
.force("link", d3.forceLink().id(function(d) { return d.id; }))
.force("charge", d3.forceManyBodySampled());
</script>In particular, it is recommended to use .velocityDecay(0.2) when using d3.forceManyBodySampled(). This helps it produce results more similar to d3.forceManyBody().
For full usage examples, see the simple example of d3-force-sampled, the d3-force-sampled speed comparison, or composing multiple forces and constraints with d3-force-sampled:
It is also possible to combine Random Vertex Sampling and the Barnes-Hut approximation. Experiments show that it creates smoother, less chaotic layouts than using Random Vertex Sampling alone.
The many-body (or n-body) force applies mutually amongst all nodes. It can be used to simulate gravity (attraction) if the strength is positive, or electrostatic charge (repulsion) if the strength is negative. This implementation uses Random Vertex Sampling to greatly improve runtime performance; the accuracy can be customized using the updateSize, sampleSize, and neighborSize parameters. The updateSize determines the number of nodes that are chosen to have new repulsive forces calculated on them during this iteration. The sampleSize determines the number of randomly nodes chosen to compute forces on a node that is being updated. The neighborSize is used to create a list of (approximate) nearest neighbors for each node that is used to calculate repulsive forces, even for nodes not chosen by the updateSize parameter.
Unlike links, which only affect two linked nodes, the charge force is global: every node can affect every other node, even if they are on disconnected subgraphs.
# d3.forceManyBodySampled() <>
Creates a new many-body force with the default parameters.
# manyBodySampled.updateSize([updateSize]) <>
If updateSize is specified, sets the updateSize accessor to the specified number or function, re-evaluates the update size accessor, and returns this force. If the update size is a number, it must be a non-negative integer; other numbers will be rounded up to the nearest non-negative integer. If the update size is a function, it will be passed the nodes array and must return an integer. The resulting number is then stored internally, such that the update size is only recomputed when the force is initialized or when this method is called with a new updateSize, and not on every application of the force. If updateSize is not specified, returns the current update size accessor, which defaults to:
function (nodes) {
return Math.pow(nodes.length, 0.75);
}The update size determines the number of nodes that are chosen to be updated at each iteration. If a node is chosen to be updated, then sampleSize nodes are randomly chosen to compute repulsive forces on it. If updateSize * sampleSize equals the number of nodes, then the algorithm will run in linear time. Using a larger updateSize or sampleSize will make the algorithm slower but more accurate. Note that this is different from the neighbor repulsive forces calculated using neighborSize, which are calculated at every iteration.
# manyBodySampled.sampleSize([sampleSize]) <>
If sampleSize is specified, sets the sampleSize accessor to the specified number or function, re-evaluates the sample size accessor, and returns this force. If the sample size is a number, it must be a non-negative integer; non-integer numbers will be rounded up to the nearest non-negative integer. If the sample size is a function, it will be passed the nodes array and must return an integer. The resulting number is then stored internally, such that the sample size is only recomputed when the force is initialized or when this method is called with a new sampleSize, and not on every application of the force. If sampleSize is not specified, returns the current sample size accessor, which defaults to:
function (nodes) {
return Math.pow(nodes.length, 0.25);
}The sample size determines the number of nodes that are chosen to compute repulsive forces on each node chosen to be updated. If updateSize * sampleSize equals the number of nodes, then the algorithm will run in linear time. Using a larger updateSize or sampleSize will make the algorithm slower but more accurate. Note that this is different from the neighbor repulsive forces calculated using neighborSize, which are calculated at every iteration.
# manyBodySampled.neighborSize([neighborSize]) <>
If neighborSize is specified, sets the neighborSize accessor to the specified number or function, re-evaluates the neighbor size accessor, and returns this force. If the neighbor size is a number, it must be a non-negative integer; non-integer numbers will be rounded up to the nearest non-negative integer. If the neighbor size is a function, it will be passed the nodes array and must return an integer. The resulting number is then stored internally, such that the neighbor size is only recomputed when the force is initialized or when this method is called with a new neighborSize, and not on every application of the force. If neighborSize is not specified, returns the current neighbor size accessor, which defaults to:
function (nodes) {
return 15;
}Each node n maintains a list of "neighbor" nodes with exactly neighborSize nodes. These neighbors are initially chosen randomly. During each iteration, the algorithm updates the node n's list of neighbors by randomly choosing a new node. If the new node is closer to n than at least one of the current nodes in the neighbor list, then the new node replaces the most distant node. Subsequently, n's neighbors are used to compute repulsive forces on n, scaled by a charge multiplier.
# manyBodySampled.chargeMultiplier([chargeMultiplier]) <>
If chargeMultiplier is specified, sets the chargeMultiplier accessor to the specified number or function, re-evaluates the neighbor size accessor, and returns this force. If the charge multiplier is a function, it will be passed the nodes array and must return an integer. The resulting number is then stored internally, such that the charge multiplier is only recomputed when the force is initialized or when this method is called with a new chargeMultiplier, and not on every application of the force. If chargeMultiplier is not specified, returns the current neighbor size accessor, which defaults to:
function (nodes) {
return return nodes.length < 100 ? 1 : nodes.length < 200 ? 3 : Math.sqrt(nodes.length);
}The charge multiplier has the effect of scaling the repulsive forces for the nodes that are chosen to update their repulsive forces, as well as the neighbors of each node. This is useful because otherwise the small number of nodes used to compute repulsive forces might not be enough to sufficiently push apart nodes.
# manyBodySampled.source([source]) <>
Sets the random number generator used as the source of randomness instead of Math.random. The given random number generator must implement the same interface as Math.random and only return values in the range [0, 1). This is useful when a seeded random number generator is preferable to Math.random. For example:
var manyBodySampled = require("d3-force-sampled"),
seedrandom = require("seedrandom");
manyBodySampled.source(seedrandom("a22ebc7c488a3a47"));# manyBodySampled.strength([strength]) <>
If strength is specified, sets the strength accessor to the specified number or function, re-evaluates the strength accessor for each node, and returns this force. A positive value causes nodes to attract each other, similar to gravity, while a negative value causes nodes to repel each other, similar to electrostatic charge. If strength is not specified, returns the current strength accessor, which defaults to:
function strength() {
return -30;
}The strength accessor is invoked for each node in the simulation, being passed the node and its zero-based index. The resulting number is then stored internally, such that the strength of each node is only recomputed when the force is initialized or when this method is called with a new strength, and not on every application of the force.
# manyBodySampled.distanceMin([distance]) <>
If distance is specified, sets the minimum distance between nodes over which this force is considered. If distance is not specified, returns the current minimum distance, which defaults to 1. A minimum distance establishes an upper bound on the strength of the force between two nearby nodes, avoiding instability. In particular, it avoids an infinitely-strong force if two nodes are exactly coincident; in this case, the direction of the force is random.
# manyBodySampled.distanceMax([distance]) <>
If distance is specified, sets the maximum distance between nodes over which this force is considered. If distance is not specified, returns the current maximum distance, which defaults to infinity. Specifying a finite maximum distance improves performance and produces a more localized layout.