# graphology/graphology-metrics

Miscellaneous graph metrics for graphology.
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centrality
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.gitignore
.travis.yml
degree.js
density.js
extent.js
index.js
modality.js
modularity.js
package.json
weighted-degree.js
weighted-size.js

# Graphology metrics

Miscellaneous metrics to be used with `graphology`.

## Installation

``````npm install graphology-metrics
``````

## Usage

Graph metrics

Node metrics

Attributes metrics

### Density

Computes the density of the given graph.

```import {density} from 'graphology-metrics';
import density from 'graphology-metrics/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 'graphology-metric/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.

### Extent

Computes the extent - min, max - of a node or edge's attribute.

```import extent from 'graphology-metrics/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 string|array: single attribute names or array of attribute names.

### Modularity

Computes the modularity, given the graph and a partitioning

```import {modularity} from 'graphology-metrics';
// Alternatively, to load only the relevant code:
import modularity from 'graphology-metrics/modularity';

// Simplest way
const Q = modularity(graph);

// If community mapping is external to the graph
const Q = modularity(graph, {
communities: {'1': 0, '2': 0, '3': 1, '4': 1, '5': 1}
});```

Arguments

• graph Graph: target graph.
• options ?object: options:
• communities ?object: object mapping nodes to their respective communities.
• 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.

### Weighted size

Computes the weighted size, i.e. the sum of the graph's edges' weight, of the given graph.

```import {weightedSize} from 'graphology-metrics';
// Alternatively, to load only the relevant code:
import weightedSize from 'graphology-metrics/weighted-size';

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.

### 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 'graphology-metrics/degree';

import degree, {
inDegree,
outDegree,
undirectedDegree,
directedDegree,
allDegree
} from 'graphology-metrics/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.

### Centrality

#### Betweenness centrality

Computes the betweenness centrality for every node.

```import betweennessCentrality from 'graphology-metrics/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 (`beetweennessCentrality`):
betweennessCentrality.assign(graph);

// To directly map the result onto a custom attribute:
betweennessCentrality.assign(graph, {attributes: '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.
• normalized ?boolean [`true`]: should the result be normalized?
• weighted ?boolean [`false`]: should we compute the weighted betweenness centrality?

#### Degree centrality

Computes the degree centrality for every node.

```import degreeCentrality from 'graphology-metrics/centrality/degree';
// Or to load more specific functions:
import {
degreeCentrality,
inDegreeCentrality,
outDegreeCentrality
} from 'graphology-metrics/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.

### Weighted degree

Computes the weighted degree of nodes. The weighted degree of a node is the sum of its edges' weights.

```import weightedDegree from 'graphology-metrics/weighted-degree';
// Or to load more specific functions:
import {
weightedDegree,
weightedInDegree,
weightedOutDegree
} from 'graphology-metrics/weighted-degree';

// 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.

### Modalities

Method returning a node categorical attribute's modalities and related statistics.

```import modalities from 'graphology-metrics/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 string|array: target categorical attribute or array of categorical attributes.
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