graphology-metrics/graph/density.js

Miscellaneous graph metrics for graphology.

/**
 * Graphology Density
 * ===================
 *
 * Functions used to compute the density of the given graph.
 */
var isGraph = require('graphology-utils/is-graph');
var simpleSize = require('./simple-size.js');

/**
 * Returns the undirected density.
 *
 * @param  {number} order - Number of nodes in the graph.
 * @param  {number} size  - Number of edges in the graph.
 * @return {number}
 */
function undirectedDensity(order, size) {
  return (2 * size) / (order * (order - 1));
}

/**
 * Returns the directed density.
 *
 * @param  {number} order - Number of nodes in the graph.
 * @param  {number} size  - Number of edges in the graph.
 * @return {number}
 */
function directedDensity(order, size) {
  return size / (order * (order - 1));
}

/**
 * Returns the mixed density.
 *
 * @param  {number} order - Number of nodes in the graph.
 * @param  {number} size  - Number of edges in the graph.
 * @return {number}
 */
function mixedDensity(order, size) {
  var d = order * (order - 1);

  return size / (d + d / 2);
}

/**
 * Returns the density for the given parameters.
 *
 * Arity 3:
 * @param  {boolean} type  - Type of density.
 * @param  {boolean} multi - Compute multi density?
 * @param  {Graph}   graph - Target graph.
 *
 * Arity 4:
 * @param  {boolean} type  - Type of density.
 * @param  {boolean} multi - Compute multi density?
 * @param  {number}  order - Number of nodes in the graph.
 * @param  {number}  size  - Number of edges in the graph.
 *
 * @return {number}
 */
function abstractDensity(type, multi, graph) {
  var order, size;

  // Retrieving order & size
  if (arguments.length > 3) {
    order = graph;
    size = arguments[3];

    if (typeof order !== 'number' || order < 0)
      throw new Error(
        'graphology-metrics/density: given order is not a valid number.'
      );

    if (typeof size !== 'number' || size < 0)
      throw new Error(
        'graphology-metrics/density: given size is not a valid number.'
      );
  } else {
    if (!isGraph(graph))
      throw new Error(
        'graphology-metrics/density: given graph is not a valid graphology instance.'
      );

    order = graph.order;
    size = graph.size;

    if (graph.multi && multi === false) size = simpleSize(graph);
  }

  // When the graph has only one node, its density is 0
  if (order < 2) return 0;

  // Guessing type & multi
  if (type === null) type = graph.type;
  if (multi === null) multi = graph.multi;

  // Getting the correct function
  var fn;

  if (type === 'undirected') fn = undirectedDensity;
  else if (type === 'directed') fn = directedDensity;
  else fn = mixedDensity;

  // Applying the function
  return fn(order, size);
}

/**
 * Exporting.
 */
exports.abstractDensity = abstractDensity;
exports.density = abstractDensity.bind(null, null, null);
exports.directedDensity = abstractDensity.bind(null, 'directed', false);
exports.undirectedDensity = abstractDensity.bind(null, 'undirected', false);
exports.mixedDensity = abstractDensity.bind(null, 'mixed', false);
exports.multiDirectedDensity = abstractDensity.bind(null, 'directed', true);
exports.multiUndirectedDensity = abstractDensity.bind(null, 'undirected', true);
exports.multiMixedDensity = abstractDensity.bind(null, 'mixed', true);