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Graphology metrics\n\nMiscellaneous metrics to be used with [`graphology`](https://graphology.github.io).\n\n## Installation\n\n```\nnpm install graphology-metrics\n```\n\n## Usage\n\n_Graph metrics_\n\n- [Density](#density)\n- [Diameter](#diameter)\n- [Extent](#extent)\n- [Modularity](#modularity)\n- [Simple size](#simple-size)\n- [Weighted size](#weighted-size)\n\n_Node metrics_\n\n- [Eccentricity](#eccentricity)\n- [Weighted degree](#weighted-degree)\n\n_Edge metrics_\n\n- [Disparity](#disparity)\n- [Simmelian strength](#simmelian-strength)\n- [Chi square](#chi-square)\n- [G square](#g-square)\n\n_Centrality_\n\n- [Betweenness centrality](#betweenness-centrality)\n- [Edge betweenness centrality](#edge-betweenness-centrality)\n- [Closeness centrality](#closeness-centrality)\n- [Degree centrality](#degree-centrality)\n- [Eigenvector centrality](#eigenvector-centrality)\n- [HITS](#hits)\n- [Pagerank](#pagerank)\n\n_Layout quality metrics_\n\n- [Connected Closeness](#connected-closeness)\n- [Edge Uniformity](#edge-uniformity)\n- [Neighborhood Preservation](#neighborhood-preservation)\n- [Stress](#stress)\n\n## Graph metrics\n\n### Density\n\nComputes the density of the given graph. Note that multi variants can exceed `0`, as it is also the case when considering self loops.\n\n```js\nimport {density} from 'graphology-metrics/graph/density';\n\n// Passing a graph instance\nconst d = density(graph);\n\n// Passing the graph's order & size\nconst d = density(order, size);\n\n// Or to force the kind of density being computed\nimport {\n  mixedDensity,\n  directedDensity,\n  undirectedDensity,\n  multiMixedDensity,\n  multiDirectedDensity,\n  multiUndirectedDensity\n} from 'graphology-metric/graph/density';\n\nconst d = undirectedDensity(mixedGraph);\n\n// If you need to chose the kind of density dynamically\nimport {abstractDensity} from 'graphology-metric/graph/density';\n\nabstractDensity('directed', true, 10, 24);\n```\n\n_Arguments_- [Chi square](#chi-square)\n\n- [G square](#g-square)\n\nEither:\n\n- **graph** _Graph_: target graph.\n\nOr:\n\n- **order** _number_: number of nodes in the graph.\n- **size** _number_: number of edges in the graph.\n\n_Abstract version arguments_\n\nEither:\n\n- **type** _string_: type of density to compute (`directed`, `undirected` or `mixed`).\n- **multi** _boolean_: whether to compute density for the multi of simple case.\n- **graph** _Graph_: target graph.\n\nOr:\n\n- **type** _string_: type of density to compute (`directed`, `undirected` or `mixed`).\n- **multi** _boolean_: whether to compute density for the multi of simple case.\n- **order** _number_: number of nodes in the graph.\n- **size** _number_: number of edges in the graph.\n\n### Diameter\n\nComputes the diameter, i.e the maximum eccentricity of any node of the given graph.\n\n```js\nimport diameter from 'graphology-metrics/graph/diameter';\n\nconst graph = new Graph();\ngraph.addNode('1');\ngraph.addNode('2');\ngraph.addNode('3');\ngraph.addUndirectedEdge(1, 2);\ngraph.addUndirectedEdge(2, 3);\n\ndiameter(graph);\n>>> 2\n\n```\n\n_Arguments_\n\n- **graph** _Graph_: target graph.\n\n### Extent\n\nComputes the extent - min, max - of a node or edge's attribute.\n\n```js\nimport {nodeExtent, edgeExtent} from 'graphology-metrics/graph';\n// Alternatively, to load only the relevant code:\nimport {nodeExtent, edgeExtent} from 'graphology-metrics/graph/extent';\n\n// Retrieving a single node attribute's extent\nnodeExtent(graph, 'size');\n>>> [1, 34]\n\n// Retrieving multiple node attributes' extents\nnodeExtent(graph, ['x', 'y']);\n>>> {x: [-4, 3], y: [-34, 56]}\n\n// The same for edges\nedgeExtent(graph, 'weight');\n>>> [0, 5.7]\n```\n\n_Arguments_\n\n- **graph** _Graph_: target graph.\n- **attributes** _string|array_: single attribute names or array of attribute names.\n\n### Modularity\n\nComputes the modularity, given the graph and a node partition. It works on both directed & undirected networks and will return the relevant modularity.\n\n```js\nimport modularity from 'graphology-metrics/graph/modularity';\n\n// Simplest way\nconst Q = modularity(graph);\n\n// Custom node partition\nconst Q = modularity(graph, {\n  getNodeCommunity(node, attr) {\n    return attr.customPartition;\n  }\n});\n```\n\n_Arguments_\n\n- **graph** _Graph_: target graph.\n- **options** _?object_: options:\n  - **getNodeCommunity** _?string\\|function_ [`community`]: name of the node community attribute or getter function.\n  - **getEdgeWeight** _?string\\|function_ [`weight`]: name of the edges' weight attribute or getter function.\n  - **resolution** _?number_: resolution parameter (`γ`).\n\n### Simple size\n\nComputes the simple size of a given graph, i.e. its number of edges if we consider the graph simple, even if it has multiple edges between pairs of nodes.\n\n```js\nimport {simpleSize} from 'graphology-metrics';\n// Alternatively, to load only the relevant code:\nimport simpleSize from 'graphology-metrics/graph/simple-size';\n\nconst graph = new MultiGraph();\ngraph.mergeEdge(1, 2);\ngraph.mergeEdge(1, 2);\ngraph.mergeEdge(4, 3);\ngraph.mergeUndirectedEdge(5, 6);\n\nsimpleSize(graph);\n>>> 3\n```\n\n### Weighted size\n\nComputes the weighted size, i.e. the sum of the graph's edges' weight, of the given graph.\n\n```js\nimport weightedSize from 'graphology-metrics/graph/weighted-size';\n\nconst graph = new Graph();\ngraph.mergeEdge(1, 2, {weight: 3});\ngraph.mergeEdge(1, 2, {weight: 1});\n\n// Simplest way\nweightedSize(graph);\n>>> 4\n\n// With custom weight attribute\nweightedSize(graph, 'myWeightAttribute');\n>>> 4\n\n// With custom getter\nweightedSize(graph, (_, attr) => attr.importance);\n```\n\n_Arguments_\n\n- **graph** _Graph_: target graph.\n- **getEdgeWeight** _?string\\|function_ [`weight`]: name of the weight attribute or getter function.\n\n## Node metrics\n\n### Weighted degree\n\nComputes the weighted degree of nodes. The weighted degree of a node is the sum of its edges' weights.\n\n```js\nimport {\n  weightedDegree,\n  weightedInDegree,\n  weightedOutDegree,\n  weightedInboundDegree,\n  weightedOutboundDegree,\n  weightedUndirectedDegree,\n  weightedDirectedDegree\n} from 'graphology-metrics/node/weighted-degree';\n\n// To compute weighted degree of a node\nweightedDegree(graph, 'A');\n\n// To use a custom weight\nweightedDegree(graph, 'A', function (_, attr) {\n  return attr.importance;\n});\n```\n\n_Arguments_\n\n- **graph** _Graph_: target graph.\n- **node** _any_: desired node.\n- **getEdgeWeight** _?string\\|function_: name of the edge weight attribute or getter function.\n\n### Eccentricity\n\nComputes the eccentricity which is the maximum of the shortest paths between the given node and any other node.\n\n```js\nimport eccentricity from 'graphology-metrics/node/eccentricity';\n\ngraph.addNode('1');\ngraph.addNode('2');\ngraph.addNode('3');\ngraph.addNode('4');\ngraph.addUndirectedEdge(1, 2);\ngraph.addUndirectedEdge(2, 3);\ngraph.addUndirectedEdge(3, 1);\ngraph.addUndirectedEdge(3, 4);\n\neccentricity(graph, 3) >> 1;\n```\n\n_Arguments_\n\n- **graph** _Graph_: target graph.\n- **node** _any_: desired node.\n\n## Edge metrics\n\n### Disparity\n\nFunction computing a score for each edge which is necessary to apply a \"disparity filter\" as described in the following paper:\n\n> Serrano, M. Ángeles, Marián Boguná, and Alessandro Vespignani. \"Extracting the multiscale backbone of complex weighted networks.\" Proceedings of the national academy of sciences 106.16 (2009): 6483-6488.\n\nNote that this metric requires a weighted graph or will return a useless result.\n\nBeware, the results must be interpreted thusly: a lower score means a more relevant edge, as is intuited in the paper's formulae. This means you can prune edges that have a score greater than a given threshold, as a statistical test. Some other implementations might differ in that they offer the opposite intuition (i.e. greater score = more relevant edge).\n\n```js\nimport disparity from 'graphology-metrics/edge/disparity';\n\n// To compute strength for every edge:\nconst disparities = disparity(graph);\n\n// To directly map the result onto edge attributes (`disparity`):\ndisparity.assign(graph);\n\n// Using custom weights\ndisparity.assign(graph, {getEdgeWeight: (_, attr) => attr.importance});\n```\n\n_Arguments_\n\n- **graph** _Graph_: target graph.\n- **options** _?object_: options:\n  - **edgeDisparityAttribute** _?string_ [`disparity`]: Name of the disparity attribute to assign.\n  - **getEdgeWeight** _?string\\|function_ [`weight`]: Name of the edge weight attribute or getter function.\n\n### Simmelian strength\n\nFunction returning the simmelian strength, i.e. the number of triangles an edge is part of, of all the edges in the given graph.\n\n```js\nimport simmelianStrength from 'graphology-metrics/edge/simmelian-strength';\n\n// To compute strength for every edge:\nconst strengths = simmelianStrength(graph);\n\n// To directly map the result onto edge attributes (`simmelianStrength`):\nsimmelianStrength.assign(graph);\n```\n\n### Chi square\n\nFunction computing a `chi square` significance test for each edge.\n\nThe test results are a `number` or `undefined`. `undefined` means the test could not be fully computed due to observed weight being less than expected. Those cases should be filtered out.\n\nTo ease filtering the edges based on the results one can use the provided `thresholds`: this object gives the minimum value of `chi square` for each level of significance expressed as `p values`.\n\n```js\nimport chiSquare from 'graphology-metrics/edge/chi-square';\n\n// To compute strength for every edge using weight attribute:\nconst chiSquareResults = chiSquare(graph);\n// To compute strength for every edge using weight custom attribute:\nconst chiSquareResults = chiSquare(graph, 'cooccurrences');\n// To compute strength for every edge defining weight as an edge function:\nconst chiSquareResults = chiSquare(graph, (_, attr) => attr.cooccurrences);\n\n// To directly map the result onto edge attribute `chiSquare`:\nchiSquare.assign(graph);\n\n// Filtering out unsignificant edges\ngraph\n  .filterEdges((_, atts) => atts.chiSquare < chiSquare.thresholds['0.01'])\n  .forEach(e => {\n    graph.dropEdge(e);\n  });\n```\n\n_Arguments_\n\n- **graph** _Graph_: target graph.\n- **getEdgeWeight** <span class=\"code\">?string\\|function</span> <span class=\"default\">weight</span>: Name of the edge weight attribute or getter function.\n\n### G square\n\nFunction computing a `g square` significance test for each edge.\n\nThe test results are a `number` or `undefined`. `undefined` means the test could not be fully computed due to observed weight being less than expected. Those cases should be filtered out.\n\nTo ease filtering the edges based on the results one can use the provided `thresholds`: this object gives the minimum value of `g square` for each level of significance expressed as `p values`.\n\n```js\nimport gSquare from 'graphology-metrics/edge/g-square';\n\n// To compute strength for every edge using weight attribute:\nconst gSquareResults = gSquare(graph);\n// To compute strength for every edge using weight custom attribute:\nconst gSquareResults = gSquare(graph, 'cooccurrences');\n// To compute strength for every edge defining weight as an edge function:\nconst gSquareResults = gSquare(graph, (_, attr) => attr.cooccurrences);\n\n// To directly map the result onto edge attribute `gSquare`:\ngSquare.assign(graph);\n\n// Filter out unsignificant edges\ngraph\n  .filterEdges((_, atts) => atts.gSquare < gSquare.thresholds['0.01'])\n  .forEach(e => {\n    graph.dropEdge(e);\n  });\n```\n\n_Arguments_\n\n- **graph** _Graph_: target graph.\n- **getEdgeWeight** <span class=\"code\">?string\\|function</span> <span class=\"default\">weight</span>: Name of the edge weight attribute or getter function.\n\n## Centrality\n\n### Betweenness centrality\n\nComputes the betweenness centrality for every node.\n\n```js\nimport betweennessCentrality from 'graphology-metrics/centrality/betweenness';\n\n// To compute centrality for every node:\nconst centralities = betweennessCentrality(graph);\n\n// To directly map the result onto nodes' attributes (`betweennessCentrality`):\nbetweennessCentrality.assign(graph);\n\n// To directly map the result onto a custom attribute:\nbetweennessCentrality.assign(graph, {nodeCentralityAttribute: 'myCentrality'});\n\n// To ignore weights\nconst centralities = betweennessCentrality(graph, {getEdgeWeight: null});\n\n// To use a getter function for weights\nconst centralities = betweennessCentrality(graph, {\n  getEdgeWeight: (_, attr) => attr.importance\n});\n```\n\n_Arguments_\n\n- **graph** _Graph_: target graph.\n- **options** _?object_: options:\n  - **nodeCentralityAttribute** _?string_ [`betweennessCentrality`]: Name of the centrality attribute to assign.\n  - **getEdgeWeight** _?string\\|function_ [`weight`]: Name of the edge weight attribute or getter function.\n  - **normalized** _?boolean_ [`true`]: should the result be normalized?\n\n### Edge betweenness centrality\n\nComputes the betweenness centrality for every edge.\n\n```js\nimport edgeBetweennessCentrality from 'graphology-metrics/centrality/edge-betweenness';\n\n// To compute centrality for every edge:\nconst centralities = edgeBetweennessCentrality(graph);\n\n// To directly map the result onto edges' attributes (`edgeBetweennessCentrality`):\nedgeBetweennessCentrality.assign(graph);\n\n// To directly map the result onto a custom attribute:\nedgeBetweennessCentrality.assign(graph, {\n  edgeCentralityAttribute: 'myCentrality'\n});\n\n// To ignore weights\nconst centralities = edgeBetweennessCentrality(graph, {getEdgeWeight: null});\n\n// To use a getter function for weights\nconst centralities = edgeBetweennessCentrality(graph, {\n  getEdgeWeight: (_, attr) => attr.importance\n});\n```\n\n_Arguments_\n\n- **graph** _Graph_: target graph.\n- **options** _?object_: options:\n  - **edgeCentralityAttribute** _?string_ [`betweennessCentrality`]: Name of the centrality attribute to assign.\n  - **getEdgeWeight** _?string\\|function_ [`weight`]: Name of the edge weight attribute or getter function.\n  - **normalized** _?boolean_ [`true`]: should the result be normalized?\n\n### Closeness centrality\n\nComputes the closeness centrality of a graph's nodes.\n\n```js\nimport closenessCentrality from 'graphology-metrics/centrality/closeness';\n\n// To compute the eigenvector centrality and return the score per node:\nconst scores = closenessCentrality(graph);\n\n// To directly map the result to nodes' attributes:\nclosenessCentrality.assign(graph);\n\n// Note that you can also pass options to customize the algorithm:\nconst p = closenessCentrality(graph, {wassermanFaust: true});\n```\n\n_Arguments_\n\n- **graph** _Graph_: target graph.\n- **options** _?object_: options:\n  - **nodeCentralityAttribute** _?string_ [`closenessCentrality`]: name of the node attribute that will be assigned the closeness centrality.\n  - **wassermanFaust** _?boolean_ [`false`]: whether to use Wasserman & Faust's normalization scheme.\n\n### Degree centrality\n\nComputes the degree centrality for every node.\n\n```js\nimport {\n  degreeCentrality,\n  inDegreeCentrality,\n  outDegreeCentrality\n} from 'graphology-metrics/centrality/degree';\n\n// To compute degree centrality for every node:\nconst centralities = degreeCentrality(graph);\n\n// To directly map the result onto nodes' attributes (`degreeCentrality`):\ndegreeCentrality.assign(graph);\n\n// To directly map the result onto a custom attribute:\ndegreeCentrality.assign(graph, {nodeCentralityAttribute: 'myCentrality'});\n```\n\n_Arguments_\n\n- **graph** _Graph_: target graph.\n- **options** _?object_: options:\n  - **nodeCentralityAttribute** _?string_ [`degreeCentrality`]: name of the centrality attribute to assign.\n\n### Eigenvector centrality\n\nComputes the eigenvector centrality of a graph's nodes.\n\n```js\nimport eigenvectorCentrality from 'graphology-metrics/centrality/eigenvector';\n\n// To compute the eigenvector centrality and return the score per node:\nconst scores = eigenvectorCentrality(graph);\n\n// To directly map the result to nodes' attributes:\neigenvectorCentrality.assign(graph);\n\n// Note that you can also pass options to customize the algorithm:\nconst p = eigenvectorCentrality(graph, {tolerance: 1e-3});\n\n// To ignore your graph's weights\neigenvectorCentrality.assign(graph, {getEdgeWeight: null});\n```\n\n_Arguments_\n\n- **graph** _Graph_: target graph.\n- **options** _?object_: options:\n  - **nodeCentralityAttribute** _?string_ [`eigenvectorCentrality`]: name of the node attribute that will be assigned the eigenvector centrality.\n  - **getEdgeWeight** _?string\\|function_ [`weight`]: name of the edges' weight attribute or getter function.\n  - **maxIterations** _?number_ [`100`]: maximum number of iterations to perform.\n  - **tolerance** _?number_ [`1.e-6`]: convergence error tolerance.\n\n### HITS\n\nComputes the hub/authority metrics for each node using the HITS algorithm.\n\n```js\nimport hits from 'graphology-metrics/centrality/hits';\n\n// To compute and return the result as 'hubs' & 'authorities':\nconst {hubs, authorities} = hits(graph);\n\n// To directly map the result to nodes' attributes:\nhits.assign(graph);\n\n// Note that you can also pass options to customize the algorithm:\nconst {hubs, authorities} = hits(graph, {normalize: false});\n```\n\n_Arguments_\n\n- **graph** _Graph_: target graph.\n- **options** _?object_: options:\n  - **getEdgeWeight** _?string\\|function_ [`weight`]: name of the edges' weight attribute or getter function.\n  - **nodeHubAttribute** _?string_ [`hub`]: name of the node attribute holding hub information.\n  - **nodeAuthorityAttribute** _?string_ [`authority`]: name of the node attribute holding authority information.\n  - **maxIterations** _?number_ [`100`]: maximum number of iterations to perform.\n  - **normalize** _?boolean_ [`true`]: should the result be normalized by the sum of values.\n  - **tolerance** _?number_ [`1.e-8`]: convergence error tolerance.\n\n### Pagerank\n\nComputes the pagerank metrics for each node.\n\n```js\nimport pagerank from 'graphology-metrics/centrality/pagerank';\n\n// To compute pagerank and return the score per node:\nconst scores = pagerank(graph);\n\n// To directly map the result to nodes' attributes:\npagerank.assign(graph);\n\n// Note that you can also pass options to customize the algorithm:\nconst p = pagerank(graph, {alpha: 0.9});\n\n// To ignore your graph's weights\npagerank.assign(graph, {getEdgeWeight: null});\n```\n\n_Arguments_\n\n- **graph** _Graph_: target graph.\n- **options** _?object_: options:\n  - **nodePagerankAttribute** _?string_ [`pagerank`]: name of the node attribute that will be assigned the pagerank score.\n  - **getEdgeWeight** _?string\\|function_ [`weight`]: name of the edges' weight attribute or getter function.\n  - **alpha** _?number_ [`0.85`]: damping parameter of the algorithm.\n  - **maxIterations** _?number_ [`100`]: maximum number of iterations to perform.\n  - **tolerance** _?number_ [`1.e-6`]: convergence error tolerance.\n\n## Layout quality metrics\n\n### Connected Closeness\n\nTODO...\n\n### Edge Uniformity\n\nComputes 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.\n\nRuns in `O(E)`.\n\n```js\nimport edgeUniformity from 'graphology-metrics/layout-quality/edge-uniformity';\n\nedgeUniformity(graph);\n>>> ~1.132\n```\n\n### Neighborhood preservation\n\nComputes 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.\n\nRuns in approximately `O(N * log(N))`.\n\n```js\nimport neighborhoodPreservation from 'graphology-metrics/layout-quality/neighborhood-preservation';\n\nneighborhoodPreservation(graph);\n// >>> 0.456\n```\n\n### Stress\n\nComputes 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.\n\nNote that this metric does not work very well when the graph has multiple connected components.\n\nNote also that this metric traverses any given graph as an undirected one.\n\nRuns in `O(N^2)`.\n\n```js\nimport stress from 'graphology-metrics/layout-quality/stress';\n\nstress(graph);\n// >>> ~24510.2914\n```","users":{}}