Graphology metrics
Miscellaneous metrics to be used with graphology
.
Installation
npm install graphologymetrics
Usage
Graph metrics
Node metrics
Attributes metrics
Layout quality metrics
Density
Computes the density of the given graph.
import {density} from 'graphologymetrics';
import density from 'graphologymetrics/density';
// Passing a graph instance
const d = density(graph);
// Passing the graph's order & size
const d = density(order, size);
// Or to force the kind of density being computed
import {
mixedDensity,
directedDensity,
undirectedDensity,
multiMixedDensity,
multiDirectedDensity,
multiUndirectedDensity
} from 'graphologymetric/density';
const d = undirectedDensity(mixedGraph);
Arguments
Either:
 graph Graph: target graph.
Or:
 order number: number of nodes in the graph.
 size number: number of edges in the graph.
Diameter
Computes the diameter, i.e the maximum eccentricity of any node of the given graph.
import {diameter} from 'graphologymetrics';
// Alternatively, to load only the relevant code:
import diameter from 'graphologymetrics/diameter';
const graph = new Graph();
graph.addNode('1');
graph.addNode('2');
graph.addNode('3');
graph.addUndirectedEdge(1, 2);
graph.addUndirectedEdge(2, 3);
diameter(graph);
>>> 2
Arguments
 graph Graph: target graph.
Extent
Computes the extent  min, max  of a node or edge's attribute.
import extent from 'graphologymetrics/extent';
// Retrieving a single node attribute's extent
extent(graph, 'size');
>>> [1, 34]
// Retrieving multiple node attributes' extents
extent(graph, ['x', 'y']);
>>> {x: [4, 3], y: [34, 56]}
// For edges
extent.edgeExtent(graph, 'weight');
>>> [0, 5.7]
Arguments
 graph Graph: target graph.
 attributes stringarray: single attribute names or array of attribute names.
Modularity
Computes the modularity, given the graph and a node partition. It works on both directed & undirected networks and will return the relevant modularity.
import {modularity} from 'graphologymetrics';
// Alternatively, to load only the relevant code:
import modularity from 'graphologymetrics/modularity';
// Simplest way
const Q = modularity(graph);
// If the partition is not given by node attributes
const Q = modularity(graph, {
communities: {'1': 0, '2': 0, '3': 1, '4': 1, '5': 1}
});
Arguments
 graph Graph: target graph.

options ?object: options:

attributes ?object: attributes' names:

community ?string [
community
]: name of the nodes' community attribute in case we need to read them from the graph itself. 
weight ?string [
weight
]: name of the edges' weight attribute.

community ?string [
 communities ?object: object mapping nodes to their respective communities.

resolution ?number: resolution parameter (
γ
). 
weighted ?boolean [
true
]: whether to compute weighted modularity or not.

attributes ?object: attributes' names:
Weighted size
Computes the weighted size, i.e. the sum of the graph's edges' weight, of the given graph.
import {weightedSize} from 'graphologymetrics';
// Alternatively, to load only the relevant code:
import weightedSize from 'graphologymetrics/weightedsize';
const graph = new Graph();
graph.mergeEdge(1, 2, {weight: 3});
graph.mergeEdge(1, 2, {weight: 1});
// Simplest way
weightedSize(graph);
>>> 4
// With custom weight attribute
weightedSize(graph, 'myWeightAttribute');
>>> 4
Arguments
 graph Graph: target graph.

weightAttribute ?string [
weight
]: name of the weight attribute.
Centrality
Betweenness centrality
Computes the betweenness centrality for every node.
import betweennessCentrality from 'graphologymetrics/centrality/betweenness';
// To compute centrality for every node:
const centrality = betweennessCentrality(graph);
// To compute weighted betweenness centrality
const centrality = betweennessCentrality(graph, {weighted: true});
// To directly map the result onto nodes' attributes (`betweennessCentrality`):
betweennessCentrality.assign(graph);
// To directly map the result onto a custom attribute:
betweennessCentrality.assign(graph, {attributes: {centrality: 'myCentrality'}});
Arguments
 graph Graph: target graph.

options ?object: options:

attributes ?object: Custom attribute names:

centrality ?string [
betweennessCentrality
]: Name of the centrality attribute to assign.  weight ?string: Name of the weight attribute.

centrality ?string [

normalized ?boolean [
true
]: should the result be normalized? 
weighted ?boolean [
false
]: should we compute the weighted betweenness centrality?

attributes ?object: Custom attribute names:
Degree centrality
Computes the degree centrality for every node.
import degreeCentrality from 'graphologymetrics/centrality/degree';
// Or to load more specific functions:
import {
degreeCentrality,
inDegreeCentrality,
outDegreeCentrality
} from 'graphologymetrics/centrality/degree';
// To compute degree centrality for every node:
const centrality = degreeCentrality(graph);
// To directly map the result onto nodes' attributes (`degreeCentrality`):
degreeCentrality.assign(graph);
// To directly map the result onto a custom attribute:
degreeCentrality.assign(graph, {attributes: {centrality: 'myCentrality'}});
Arguments
 graph Graph: target graph.

options ?object: options:

attributes ?object: custom attribute names:

centrality ?string [
degreeCentrality
]: name of the centrality attribute to assign.

centrality ?string [

attributes ?object: custom attribute names:
Weighted degree
Computes the weighted degree of nodes. The weighted degree of a node is the sum of its edges' weights.
import weightedDegree from 'graphologymetrics/weighteddegree';
// Or to load more specific functions:
import {
weightedDegree,
weightedInDegree,
weightedOutDegree
} from 'graphologymetrics/weighteddegree';
// To compute weighted degree of a single node
weightedDegree(graph, 'A');
// To compute weighted degree of every node
const weightedDegrees = weightedDegree(graph);
// To compute normalized weighted degree, i.e. weighted degree will be
// divided by the node's relevant degree
weightedDegree(graph, 'A', {normalized: true});
// To directly map the result onto node attributes
weightedDegree.assign(graph);
Arguments
To compute the weighted degree of a single node:
 graph Graph: target graph.
 node any: desired node.
 options ?object: options. See below.
To compute the weighted degree of every node:
 graph Graph: target graph.
 options ?object: options. See below.
Options

attributes ?object: custom attribute names:

weight ?string [
weight
]: name of the weight attribute. 
weightedDegree ?string [
weightedDegree
]: name of the attribute to assign.

weight ?string [
Degree
Returns degree information for every node in the graph. Note that graphology
's API already gives you access to this information through #.degree
etc. So only consider this function as a convenience to extract/assign all degrees at once.
import degree from 'graphologymetrics/degree';
import degree, {
inDegree,
outDegree,
undirectedDegree,
directedDegree,
allDegree
} from 'graphologymetrics/degree';
// To extract degree information for every node
const degrees = degree(graph);
>>> {node1: 34, node2: 45, ...}
// To extract only in degree information for every node
const inDegrees = inDegree(graph);
// To extract full degree breakdown for every node
const degrees = allDegree(graph);
>>> { // Assuming the graph is directed
node1: {
inDegree: 2,
outDegree: 36
},
...
}
// To map degree information to node attributes
degree.assign(graph);
graph.getNodeAttribute(node, 'degree');
>>> 45
// To map only degree & in degree to node attributes
allDegree.assign(graph, {types: ['degree', 'inDegree']});
// To map only degree & in degree with different names
allDegree(
graph,
{
attributes: {
inDegree: 'in',
outDegree: 'out'
},
types: ['inDegree', 'outDegree']
}
)
>>> {
1: {in: 1, out: 1},
...
}
Arguments
 graph Graph: target graph.

options ?object: options:

attributes ?object: Custom attribute names:
 degree ?string: Name of the mixed degree attribute.
 inDegree ?string: Name of the mixed inDegree attribute.
 outDegree ?string: Name of the mixed outDegree attribute.
 undirectedDegree ?string: Name of the mixed undirectedDegree attribute.
 directedDegree ?string: Name of the mixed directedDegree attribute.
 types ?array: List of degree types to extract.

attributes ?object: Custom attribute names:
Eccentricity
Computes the eccentricity which is the maximum of the shortest paths between the given node and any other node.
import {eccentricity} from 'graphologymetrics';
// Alternatively, to load only the relevant code:
import eccentricity from 'graphologymetrics/eccentricity';
graph.addNode('1');
graph.addNode('2');
graph.addNode('3');
graph.addNode('4');
graph.addUndirectedEdge(1, 2);
graph.addUndirectedEdge(2, 3);
graph.addUndirectedEdge(3, 1);
graph.addUndirectedEdge(3, 4);
eccentricity(graph, 3)
>> 1
Arguments
 graph Graph: target graph.
 node any: desired node.
Modalities
Method returning a node categorical attribute's modalities and related statistics.
import modalities from 'graphologymetrics/modalities';
// Retrieving the 'type' attribute's modalities
const info = modalities(graph, 'type');
>>> {
value1: {
nodes: 34,
internalEdges: 277,
internalDensity: 0.03,
externalEdges: 45,
externalDensity: 0.05,
inboundEdges: 67,
inboundDensity: 0.07,
outboundEdges: 124,
outboundDensity: 0.003
},
...
}
// Retrieving modalities info for several attributes at once
const info = modalities(graph, ['type', 'lang']);
>>> {
type: {...},
lang: {...}
}
Arguments
 graph Graph: target graph.
 attribute stringarray: target categorical attribute or array of categorical attributes.
Edge Uniformity
Computes the edge uniformity layout quality metric from the given graph having x
and y
positions attached to its nodes. Edge uniformity is the normalized standard deviation of edge length of the graph. Lower values should be synonym of better layout according to this particular metric.
Runs in O(E)
.
import edgeUniformity from 'graphologymetrics/layoutquality/edgeuniformity';
edgeUniformity(graph);
>>> ~1.132
Neighborhood preservation
Computes the "neighborhood preservation" layout quality metric from the given graph having x
and y
positions attached to its nodes. Neighborhood preservation is the average proportion of node neighborhood being the same both in the graph's topology and its 2d layout space. The metric is therefore comprised between 0
and 1
, 1
being the best, meaning that every node keeps its neighborhood perfectly intact within the layout space.
Runs in approximately O(N * log(N))
.
import neighborhoodPreservation from 'graphologymetrics/layoutquality/neighborhoodpreservation';
neighborhoodPreservation(graph);
// >>> 0.456
Stress
Computes the "stress" layout quality metric from the given graph having x
and y
positions attached to its nodes. Stress is the sum of normalized delta between node topology distances and their layout space distances. Lower values should be synonym of better layout according to this particular metric.
Note that this metric does not work very well when the graph has multiple connected components.
Note also that this metric traverses any given graph as an undirected one.
Runs in O(N^2)
.
import stress from 'graphologymetrics/layoutquality/stress';
stress(graph);
// >>> ~24510.2914