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Graph Functions

Utility functions available for named graphs

This chapter describes various functions on a graph. A lot of these accept a vertex (or edge) example as parameter as defined in the next section.

Examples explain the API using the City Graph:

Social Example Graph

Definition of examples

For many of the following functions examples can be passed in as a parameter. Examples are used to filter the result set for objects that match the conditions. These examples can have the following values:

  • null, there is no matching executed all found results are valid.
  • A string, only results are returned, which _id equal the value of the string
  • An example object, defining a set of attributes. Only results having these attributes are matched.
  • A list containing example objects and/or strings. All results matching at least one of the elements in the list are returned.

Get vertices from edges

Get the source vertex of an edge

graph._fromVertex(edgeId)

Returns the vertex defined with the attribute _from of the edge with edgeId as its _id.

  • edgeId (required): _id attribute of the edge

Examples

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("social");
var any = require("@arangodb").db.relation.any();
graph._fromVertex("relation/" + any._key);
Show output

Get the target vertex of an edge

graph._toVertex(edgeId)

Returns the vertex defined with the attribute _to of the edge with edgeId as its _id.

  • edgeId (required): _id attribute of the edge

Examples

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("social");
var any = require("@arangodb").db.relation.any();
graph._toVertex("relation/" + any._key);
Show output

_neighbors

Get all neighbors of the vertices defined by the example.

graph._neighbors(vertexExample, options)

The function accepts an id, an example, a list of examples or even an empty example as parameter for vertexExample. The complexity of this method is O(n * m^x) with n being the vertices defined by the vertexExample parameter, the average amount of neighbors m, and the maximal depths x. Hence, the default call has a complexity of O(n * m);

  • vertexExample (optional): See Definition of examples
  • options (optional): An object defining further options. Can have the following values:
    • direction: The direction of the edges. Possible values are "outbound", "inbound", and "any" (default).
    • edgeExamples: Filter the edges, see Definition of examples
    • neighborExamples: Filter the neighbor vertices, see Definition of examples
    • edgeCollectionRestriction: One or a list of edge-collection names that should be considered to be on the path.
    • vertexCollectionRestriction: One or a list of vertex-collection names that should be considered on the intermediate vertex steps.
    • minDepth: Defines the minimal number of intermediate steps to neighbors (default is 1).
    • maxDepth: Defines the maximal number of intermediate steps to neighbors (default is 1).

Examples

A route planner example, all neighbors of capitals.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._neighbors({isCapital : true});
Show output

A route planner example, all outbound neighbors of Hamburg.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._neighbors('germanCity/Hamburg', {direction : 'outbound', maxDepth : 2});
Show output

_commonNeighbors

Get all common neighbors of the vertices defined by the examples.

graph._commonNeighbors(vertex1Example, vertex2Examples, optionsVertex1, optionsVertex2)

This function returns the intersection of graph_module._neighbors(vertex1Example, optionsVertex1) and graph_module._neighbors(vertex2Example, optionsVertex2). For parameter documentation see _neighbors.

The complexity of this method is O(n*m^x) with n being the maximal amount of vertices defined by the parameters vertexExamples, m the average amount of neighbors and x the maximal depths. Hence the default call would have a complexity of O(n*m);

Examples

A route planner example, all common neighbors of capitals.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._commonNeighbors({isCapital : true}, {isCapital : true});
Show output

A route planner example, all common outbound neighbors of Hamburg with any other location which have a maximal depth of 2 :

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._commonNeighbors(
  'germanCity/Hamburg',
  {},
  {direction : 'outbound', maxDepth : 2},
  {direction : 'outbound', maxDepth : 2});
Show output

_countCommonNeighbors

Get the amount of common neighbors of the vertices defined by the examples.

graph._countCommonNeighbors(vertex1Example, vertex2Examples, optionsVertex1, optionsVertex2)

Similar to _commonNeighbors but returns count instead of the elements.

Examples

A route planner example, all common neighbors of capitals.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
var example = { isCapital: true };
var options = { includeData: true };
graph._countCommonNeighbors(example, example, options, options);
Show output

A route planner example, all common outbound neighbors of Hamburg with any other location which have a maximal depth of 2 :

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
var options = { direction: 'outbound', maxDepth: 2, includeData: true };
graph._countCommonNeighbors('germanCity/Hamburg', {}, options, options);
Show output

_commonProperties

Get the vertices of the graph that share common properties.

graph._commonProperties(vertex1Example, vertex2Examples, options)

The function accepts an id, an example, a list of examples or even an empty example as parameter for vertex1Example and vertex2Example.

The complexity of this method is O(n) with n being the maximal amount of vertices defined by the parameters vertexExamples.

  • vertex1Examples (optional): Filter the set of source vertices, see Definition of examples

  • vertex2Examples (optional): Filter the set of vertices compared to, see Definition of examples

  • options (optional) An object defining further options. Can have the following values:

    • vertex1CollectionRestriction : One or a list of vertex-collection names that should be searched for source vertices.
    • vertex2CollectionRestriction : One or a list of vertex-collection names that should be searched for compare vertices.
    • ignoreProperties : One or a list of attribute names of a document that should be ignored.

Examples

A route planner example, all locations with the same properties:

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._commonProperties({}, {});
Show output

A route planner example, all cities which share same properties except for population.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._commonProperties({}, {}, { ignoreProperties: 'population' });
Show output

_countCommonProperties

Get the amount of vertices of the graph that share common properties.

graph._countCommonProperties(vertex1Example, vertex2Examples, options)

Similar to _commonProperties but returns count instead of the objects.

Examples

A route planner example, all locations with the same properties:

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._countCommonProperties({}, {});
Show output

A route planner example, all German cities which share same properties except for population.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._countCommonProperties({}, {}, {
  vertex1CollectionRestriction: 'germanCity',
  vertex2CollectionRestriction: 'germanCity',
  ignoreProperties: 'population'
});
Show output

_paths

The _paths function returns all paths of a graph.

graph._paths(options)

This function determines all available paths in a graph.

The complexity of this method is O(n*n*m) with n being the amount of vertices in the graph and m the average amount of connected edges;

  • options (optional): An object containing options, see below:
    • direction: The direction of the edges. Possible values are "any", "inbound", and "outbound" (default).
    • followCycles (optional): If set to true the query follows cycles in the graph, default is false.
    • minLength (optional): Defines the minimal length a path must have to be returned (default is 0).
    • maxLength (optional): Defines the maximal length a path must have to be returned (default is 10).

Examples

Return all paths of the graph “social”:

var examples = require("@arangodb/graph-examples/example-graph");
var g = examples.loadGraph("social");
g._paths();
Show output

Return all inbound paths of the graph “social” with a maximal length of 1 and a minimal length of 2:

var examples = require("@arangodb/graph-examples/example-graph");
var g = examples.loadGraph("social");
g._paths({ direction: 'inbound', minLength: 1, maxLength: 2 });
Show output

_shortestPath

The _shortestPath function returns all shortest paths of a graph.

graph._shortestPath(startVertexExample, endVertexExample, options)

This function determines all shortest paths in a graph. The function accepts an id, an example, a list of examples or even an empty example as parameter for start and end vertex. The length of a path is by default the amount of edges from one start vertex to an end vertex. The option weight allows the user to define an edge attribute representing the length.

  • startVertexExample (optional): An example for the desired start Vertices (see Definition of examples).
  • endVertexExample (optional): An example for the desired end Vertices (see Definition of examples).
  • options (optional): An object containing options, see below:
    • direction: The direction of the edges as a string. Possible values are "outbound", "inbound", and "any" (default).
    • edgeCollectionRestriction: One or multiple edge collection names. Only edges from these collections will be considered for the path.
    • startVertexCollectionRestriction: One or multiple vertex collection names. Only vertices from these collections will be considered as start vertex of a path.
    • endVertexCollectionRestriction: One or multiple vertex collection names. Only vertices from these collections will be considered as end vertex of a path.
    • weight: The name of the attribute of the edges containing the length as a string.
    • defaultWeight: Only used with the option weight. If an edge does not have the attribute named as defined in option weight this default is used as length. If no default is supplied the default would be positive Infinity so the path could not be calculated.

Examples

A route planner example, shortest path from all german to all french cities:

var examples = require("@arangodb/graph-examples/example-graph");
var g = examples.loadGraph("routeplanner");
g._shortestPath({}, {}, {
  weight: 'distance',
  endVertexCollectionRestriction: 'frenchCity',
  startVertexCollectionRestriction: 'germanCity'
});
Show output

A route planner example, shortest path from Hamburg and Cologne to Lyon:

var examples = require("@arangodb/graph-examples/example-graph");
var g = examples.loadGraph("routeplanner");
g._shortestPath([
  {_id: 'germanCity/Cologne'},
  {_id: 'germanCity/Munich'}
], 'frenchCity/Lyon', { weight: 'distance' });
Show output

_distanceTo

The _distanceTo function returns all paths and there distance within a graph.

graph._distanceTo(startVertexExample, endVertexExample, options)

This function is a wrapper of graph._shortestPath. It does not return the actual path but only the distance between two vertices.

Examples

A route planner example, shortest distance from all german to all french cities:

var examples = require("@arangodb/graph-examples/example-graph");
var g = examples.loadGraph("routeplanner");
g._distanceTo({}, {}, {
  weight: 'distance',
  endVertexCollectionRestriction: 'frenchCity',
  startVertexCollectionRestriction: 'germanCity'
});
Show output

A route planner example, shortest distance from Hamburg and Cologne to Lyon:

var examples = require("@arangodb/graph-examples/example-graph");
var g = examples.loadGraph("routeplanner");
g._distanceTo([
  {_id: 'germanCity/Cologne'},
  {_id: 'germanCity/Munich'}
], 'frenchCity/Lyon', { weight: 'distance' });
Show output

_absoluteEccentricity

Get the eccentricity  of the vertices defined by the examples.

graph._absoluteEccentricity(vertexExample, options)

The function accepts an id, an example, a list of examples or even an empty example as parameter for vertexExample.

  • vertexExample (optional): Filter the vertices, see Definition of examples
  • options (optional): An object defining further options. Can have the following values:
    • direction: The direction of the edges. Possible values are "outbound", "inbound", and "any" (default).
    • edgeCollectionRestriction : One or a list of edge-collection names that should be considered to be on the path.
    • startVertexCollectionRestriction : One or a list of vertex-collection names that should be considered for source vertices.
    • endVertexCollectionRestriction : One or a list of vertex-collection names that should be considered for target vertices.
    • weight: The name of the attribute of the edges containing the weight.
    • defaultWeight: Only used with the option weight. If an edge does not have the attribute named as defined in option weight this default is used as weight. If no default is supplied the default would be positive infinity so the path and hence the eccentricity cannot be calculated.

Examples

A route planner example, the absolute eccentricity of all locations.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._absoluteEccentricity({});
Show output

A route planner example, the absolute eccentricity of all locations. This considers the actual distances.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._absoluteEccentricity({}, { weight: 'distance' });
Show output

A route planner example, the absolute eccentricity of all cities regarding only outbound paths.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._absoluteEccentricity({}, {
  startVertexCollectionRestriction: 'germanCity',
  direction: 'outbound',
  weight: 'distance'
});
Show output

_eccentricity

Get the normalized eccentricity  of the vertices defined by the examples.

graph._eccentricity(vertexExample, options)

Similar to _absoluteEccentricity but returns a normalized result.

Examples

A route planner example, the eccentricity of all locations.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._eccentricity();
Show output

A route planner example, the weighted eccentricity.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._eccentricity({ weight: 'distance' });
Show output

_absoluteCloseness

Get the closeness  of the vertices defined by the examples.

graph._absoluteCloseness(vertexExample, options)

The function accepts an id, an example, a list of examples or even an empty example as parameter for vertexExample.

  • vertexExample (optional): Filter the vertices, see Definition of examples
  • options (optional) An object defining further options. Can have the following values:
    • direction: The direction of the edges. Possible values are "outbound", "inbound", and "any" (default).
    • edgeCollectionRestriction : One or a list of edge-collection names that should be considered to be on the path.
    • startVertexCollectionRestriction : One or a list of vertex-collection names that should be considered for source vertices.
    • endVertexCollectionRestriction : One or a list of vertex-collection names that should be considered for target vertices.
    • weight: The name of the attribute of the edges containing the weight.
    • defaultWeight: Only used with the option weight. If an edge does not have the attribute named as defined in option weight this default is used as weight. If no default is supplied the default would be positive infinity so the path and hence the closeness cannot be calculated.

Examples

A route planner example, the absolute closeness of all locations.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._absoluteCloseness({});
Show output

A route planner example, the absolute closeness of all locations. This considers the actual distances.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._absoluteCloseness({}, { weight: 'distance' });
Show output

A route planner example, the absolute closeness of all German Cities regarding only outbound paths.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._absoluteCloseness({}, {
  startVertexCollectionRestriction: 'germanCity',
  direction: 'outbound',
  weight: 'distance'
});
Show output

_closeness

Get the normalized closeness  of graphs vertices.

graph._closeness(options)

Similar to _absoluteCloseness but returns a normalized value.

Examples

A route planner example, the normalized closeness of all locations.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._closeness();
Show output

A route planner example, the closeness of all locations. This considers the actual distances.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._closeness({ weight: 'distance' });
Show output

A route planner example, the closeness of all cities regarding only outbound paths.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._closeness({ direction: 'outbound', weight: 'distance' });
Show output

_absoluteBetweenness

Get the betweenness  of all vertices in the graph.

graph._absoluteBetweenness(vertexExample, options)

  • vertexExample (optional): Filter the vertices, see Definition of examples
  • options (optional): An object defining further options. Can have the following values:
    • direction: The direction of the edges. Possible values are "outbound", "inbound", and "any" (default).
    • weight: The name of the attribute of the edges containing the weight.
    • defaultWeight: Only used with the option weight. If an edge does not have the attribute named as defined in option weight this default is used as weight. If no default is supplied the default would be positive infinity so the path and hence the betweenness cannot be calculated.

Examples

A route planner example, the absolute betweenness of all locations.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._absoluteBetweenness({});
Show output

A route planner example, the absolute betweenness of all locations. This considers the actual distances.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._absoluteBetweenness({ weight: 'distance' });
Show output

A route planner example, the absolute betweenness of all cities regarding only outbound paths.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._absoluteBetweenness({ direction: 'outbound', weight: 'distance' });
Show output

_betweenness

Get the normalized betweenness  of graphs vertices.

graph_module._betweenness(options)

Similar to _absoluteBetweenness but returns normalized values.

Examples

A route planner example, the betweenness of all locations.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._betweenness();
Show output

A route planner example, the betweenness of all locations. This considers the actual distances.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._betweenness({ weight: 'distance' });
Show output

A route planner example, the betweenness of all cities regarding only outbound paths.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._betweenness({ direction: 'outbound', weight: 'distance' });
Show output

_radius

Get the radius  of a graph.

  • options (optional): An object defining further options. Can have the following values:
    • direction: The direction of the edges. Possible values are "outbound", "inbound", and "any" (default).
    • weight: The name of the attribute of the edges containing the weight.
    • defaultWeight: Only used with the option weight. If an edge does not have the attribute named as defined in option weight this default is used as weight. If no default is supplied the default would be positive infinity so the path and hence the radius cannot be calculated.

Examples

A route planner example, the radius of the graph.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._radius();
Show output

A route planner example, the radius of the graph. This considers the actual distances.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._radius({ weight: 'distance' });
Show output

A route planner example, the radius of the graph regarding only outbound paths.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._radius({ direction: 'outbound', weight: 'distance' });
Show output

_diameter

Get the diameter  of a graph.

graph._diameter(graphName, options)

  • options (optional): An object defining further options. Can have the following values:
    • direction: The direction of the edges. Possible values are "outbound", "inbound", and "any" (default).
    • weight: The name of the attribute of the edges containing the weight.
    • defaultWeight: Only used with the option weight. If an edge does not have the attribute named as defined in option weight this default is used as weight. If no default is supplied the default would be positive infinity so the path and hence the radius cannot be calculated.

Examples

A route planner example, the diameter of the graph.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._diameter();
Show output

A route planner example, the diameter of the graph. This considers the actual distances.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._diameter({ weight: 'distance' });
Show output

A route planner example, the diameter of the graph regarding only outbound paths.

var examples = require("@arangodb/graph-examples/example-graph");
var graph = examples.loadGraph("routeplanner");
graph._diameter({ direction: 'outbound', weight: 'distance' });
Show output

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