Graph traversals in AQL

Syntax

There are two slightly different syntaxes for traversals in AQL, one for

• named graphs and another to
• specify a set of edge collections (anonymous graph).

Working with named graphs

The syntax for AQL graph traversals using named graphs is as follows (square brackets denote optional parts and | denotes alternatives):

FOR vertex[, edge[, path]]
  IN [min[..max]]
  OUTBOUND|INBOUND|ANY startVertex
  GRAPH graphName
  [PRUNE [pruneVariable = ]pruneCondition]
  [OPTIONS options]

• FOR: emits up to three variables:
  • vertex (object): the current vertex in a traversal
  • edge (object, optional): the current edge in a traversal
  • path (object, optional): representation of the current path with two members:
    • vertices: an array of all vertices on this path
    • edges: an array of all edges on this path
• IN min..max: the minimal and maximal depth for the traversal:
  • min (number, optional): edges and vertices returned by this query start at the traversal depth of min (thus edges and vertices below it are not returned). If not specified, it defaults to 1. The minimal possible value is 0.
  • max (number, optional): up to max length paths are traversed. If omitted, max defaults to min. Thus only the vertices and edges in the range of min are returned. max cannot be specified without min.
• OUTBOUND|INBOUND|ANY: follow outgoing, incoming, or edges pointing in either direction in the traversal. Note that this can’t be replaced by a bind parameter.
• startVertex (string|object): a vertex where the traversal originates from. This can be specified in the form of an ID string or in the form of a document with the _id attribute. All other values lead to a warning and an empty result. If the specified document does not exist, the result is empty as well and there is no warning.
• GRAPH graphName (string): the name identifying the named graph. Its vertex and edge collections are looked up. Note that the graph name is like a regular string, hence it must be enclosed by quote marks, like GRAPH "graphName".
• PRUNE expression (AQL expression, optional): An expression, like in a FILTER statement, which is evaluated in every step of the traversal, as early as possible. The semantics of this expression are as follows:
  • If the expression evaluates to false, the traversal continues on the current path.
  • If the expression evaluates to true, the traversal does not continue on the current path. However, the paths up to this point are considered as a result (they might still be post-filtered or ignored due to depth constraints). For example, a traversal over the graph (A) -> (B) -> (C) starting at A and pruning on B results in (A) and (A) -> (B) being valid paths, whereas (A) -> (B) -> (C) is not returned because it gets pruned on B.

  You can only use a single PRUNE clause per FOR traversal operation, but the prune expression can contain an arbitrary number of conditions using AND and OR statements for complex expressions. You can use the variables emitted by the FOR operation in the prune expression, as well as all variables defined before the traversal.

  You can optionally assign the prune expression to a variable like PRUNE var = <expr> to use the evaluated result elsewhere in the query, typically in a FILTER expression.

  See Pruning for details.

• OPTIONS options (object, optional): used to modify the execution of the traversal. Only the following attributes have an effect, all others are ignored:
  • order (string): optionally specify which traversal algorithm to use
    • "bfs" – the traversal is executed breadth-first. The results first contain all vertices at depth 1, then all vertices at depth 2 and so on.
    • "dfs" (default) – the traversal is executed depth-first. It first returns all paths from min depth to max depth for one vertex at depth 1, then for the next vertex at depth 1 and so on.
    • "weighted" - the traversal is a weighted traversal (introduced in v3.8.0). Paths are enumerated with increasing cost. Also see weightAttribute and defaultWeight. A returned path has an additional attribute weight containing the cost of the path after every step. The order of paths having the same cost is non-deterministic. Negative weights are not supported and abort the query with an error.
  • bfs (bool): deprecated, use order: "bfs" instead.
  • uniqueVertices (string): optionally ensure vertex uniqueness
    • "path" – it is guaranteed that there is no path returned with a duplicate vertex
    • "global" – it is guaranteed that each vertex is visited at most once during the traversal, no matter how many paths lead from the start vertex to this one. If you start with a min depth > 1 a vertex that was found before min depth might not be returned at all (it still might be part of a path). It is required to set order: "bfs" or order: "weighted" because with depth-first search the results would be unpredictable. Note: Using this configuration the result is not deterministic any more. If there are multiple paths from startVertex to vertex, one of those is picked. In case of a weighted traversal, the path with the lowest weight is picked, but in case of equal weights it is undefined which one is chosen.
    • "none" (default) – no uniqueness check is applied on vertices
  • uniqueEdges (string): optionally ensure edge uniqueness
    • "path" (default) – it is guaranteed that there is no path returned with a duplicate edge
    • "none" – no uniqueness check is applied on edges. Note: Using this configuration, the traversal follows edges in cycles.
  • edgeCollections (string|array): Optionally restrict edge collections the traversal may visit (introduced in v3.7.0). If omitted, or an empty array is specified, then there are no restrictions.
    • A string parameter is treated as the equivalent of an array with a single element.
    • Each element of the array should be a string containing the name of an edge collection.
  • vertexCollections (string|array): Optionally restrict vertex collections the traversal may visit (introduced in v3.7.0). If omitted, or an empty array is specified, then there are no restrictions.
    • A string parameter is treated as the equivalent of an array with a single element.
    • Each element of the array should be a string containing the name of a vertex collection.
    • The starting vertex is always allowed, even if it does not belong to one of the collections specified by a restriction.

  • parallelism (number, optional): Optionally parallelize traversal execution (introduced in v3.7.1). If omitted or set to a value of 1, traversal execution is not parallelized. If set to a value greater than 1, then up to that many worker threads can be used for concurrently executing the traversal. The value is capped by the number of available cores on the target machine.

    Parallelizing a traversal is normally useful when there are many inputs (start vertices) that the nested traversal can work on concurrently. This is often the case when a nested traversal is fed with several tens of thousands of start vertices, which can then be distributed randomly to worker threads for parallel execution.

    Traversal parallelization is only available in the Enterprise Edition, including the ArangoGraph Insights Platform.

  • maxProjections (number, optional): Specifies the number of document attributes per FOR loop to be used as projections. The default value is 5.

    Traversal projections are only available in the Enterprise Edition, including the ArangoGraph Insights Platform.

  • weightAttribute (string, optional): Specifies the name of an attribute that is used to look up the weight of an edge. If no attribute is specified or if it is not present in the edge document then the defaultWeight is used. The attribute value must not be negative.
  • defaultWeight (number, optional): Specifies the default weight of an edge. The value must not be negative. The default value is 1.

Working with collection sets

The syntax for AQL graph traversals using collection sets is as follows (square brackets denote optional parts and | denotes alternatives):

[WITH vertexCollection1[, vertexCollection2[, vertexCollectionN]]]
FOR vertex[, edge[, path]]
  IN [min[..max]]
  OUTBOUND|INBOUND|ANY startVertex
  edgeCollection1[, edgeCollection2[, edgeCollectionN]]
  [PRUNE [pruneVariable = ]pruneCondition]
  [OPTIONS options]

• WITH: Declaration of collections. Optional for single server instances, but required for graph traversals in a cluster. Needs to be placed at the very beginning of the query.
  • collections (collection, repeatable): list of vertex collections that are involved in the traversal

• edgeCollections (collection, repeatable): One or more edge collections to use for the traversal (instead of using a named graph with GRAPH graphName). Vertex collections are determined by the edges in the edge collections.

  You can override the default traversal direction by setting OUTBOUND, INBOUND, or ANY before any of the edge collections.

  If the same edge collection is specified multiple times, it behaves as if it were specified only once. Specifying the same edge collection is only allowed when the collections do not have conflicting traversal directions.

  Views cannot be used as edge collections.

• See the named graph variant for the remaining traversal parameters. The edgeCollections restriction option is redundant in this case.

Traversing in mixed directions

For traversals with a list of edge collections you can optionally specify the direction for some of the edge collections. Say for example you have three edge collections edges1, edges2 and edges3, where in edges2 the direction has no relevance but in edges1 and edges3 the direction should be taken into account. In this case you can use OUTBOUND as general traversal direction and ANY specifically for edges2 as follows:

FOR vertex IN OUTBOUND
  startVertex
  edges1, ANY edges2, edges3

All collections in the list that do not specify their own direction use the direction defined after IN. This allows to use a different direction for each collection in your traversal.

Graph traversals in a cluster

Due to the nature of graphs, edges may reference vertices from arbitrary collections. Following the paths can thus involve documents from various collections and it is not possible to predict which are visited in a traversal. Which collections need to be loaded by the graph engine can only be determined at run time.

Use the WITH statement to specify the collections you expect to be involved. This is required for traversals using collection sets in cluster deployments.

Pruning

You can define stop conditions for graph traversals to return specific data and to improve the query performance. This is called pruning and works by checking conditions during the traversal as opposed to filtering the results afterwards (post-filtering). This reduces the amount of data to be checked by stopping the traversal down specific paths early.

You can specify one PRUNE expression per graph traversal, but it can contain an arbitrary number of conditions. You can use the vertex, edge, and path variables emitted by the traversal in a prune expression, as well as all other variables defined before the FOR operation. Note that PRUNE is an optional clause of the FOR operation and that the OPTIONS clause needs to be placed after PRUNE.

FOR v, e, p IN 0..10 OUTBOUND "places/Toronto" GRAPH "kShortestPathsGraph"
      PRUNE v.label == "Edmonton"
      OPTIONS { uniqueVertices: "path" }
      RETURN CONCAT_SEPARATOR(" -- ", p.vertices[*].label)

[
  "Toronto",
  "Toronto -- Winnipeg",
  "Toronto -- Winnipeg -- Saskatoon",
  "Toronto -- Winnipeg -- Saskatoon -- Edmonton"
]

The above example shows a graph traversal using a train station and connections dataset:

The traversal starts at Toronto (bottom left), the traversal depth is limited to 10, and every station is only visited once. The traversal could continue up to Vancouver (bottom right) at depth 5, but it is stopped early on this path (the only path in this example) at Edmonton because of the prune expression.

The traversal along paths is stopped as soon as the prune expression evaluates to true for a given path. The current depth is still included in the result, however. This can be seen in the query result of the example which includes the Edmonton vertex at which it stopped.

The following example starts a traversal at London (middle right), with a depth between 2 and 3, and every station is only visited once. The station names as well as the travel times are returned:

FOR v, e, p IN 2..3 OUTBOUND "places/London" GRAPH "kShortestPathsGraph"
      OPTIONS { uniqueVertices: "path" }
      RETURN CONCAT_SEPARATOR(" -- ", INTERLEAVE(p.vertices[*].label, p.edges[*].travelTime))

[
  "London -- 2.5 -- Brussels -- 2 -- Cologne",
  "London -- 2 -- York -- 3.5 -- Carlisle",
  "London -- 2 -- York -- 3.5 -- Carlisle -- 2 -- Birmingham",
  "London -- 2 -- York -- 3.5 -- Carlisle -- 1 -- Glasgow",
  "London -- 2 -- York -- 4 -- Edinburgh",
  "London -- 2 -- York -- 4 -- Edinburgh -- 1 -- Glasgow",
  "London -- 2 -- York -- 4 -- Edinburgh -- 3 -- Leuchars",
  "London -- 2.5 -- Birmingham -- 1 -- Carlisle",
  "London -- 2.5 -- Birmingham -- 1 -- Carlisle -- 2.5 -- York",
  "London -- 2.5 -- Birmingham -- 1 -- Carlisle -- 1 -- Glasgow"
]

The same example with an added prune expression, with vertex and edge conditions:

FOR v, e, p IN 2..3 OUTBOUND "places/London" GRAPH "kShortestPathsGraph"
      PRUNE v.label == "Carlisle" OR e.travelTime > 3
      OPTIONS { uniqueVertices: "path" }
      RETURN CONCAT_SEPARATOR(" -- ", INTERLEAVE(p.vertices[*].label, p.edges[*].travelTime))

[
  "London -- 2.5 -- Brussels -- 2 -- Cologne",
  "London -- 2 -- York -- 3.5 -- Carlisle",
  "London -- 2 -- York -- 4 -- Edinburgh",
  "London -- 2.5 -- Birmingham -- 1 -- Carlisle"
]

If either the Carlisle vertex or an edge with a travel time of over three hours is encountered, the subsequent paths are pruned. In the example, this removes the train connections to Birmingham, Glasgow, and York, which come after Carlisle, as well as the connections to and via Edinburgh because of the four hour duration for the section from York to Edinburgh.

If your graph is comprised of multiple vertex or edge collections, you can also prune as soon as you reach a certain collection, using a condition like PRUNE IS_SAME_COLLECTION("stopCollection", v).

If you want to only return the results of the depth at which the traversal stopped due to the prune expression, you can use a FILTER in addition. You can assign the evaluated result of a prune expression to a variable (PRUNE var = <expr>) and use it for filtering:

FOR v, e, p IN 2..3 OUTBOUND "places/London" GRAPH "kShortestPathsGraph"
      PRUNE cond = v.label == "Carlisle" OR e.travelTime > 3
      OPTIONS { uniqueVertices: "path" }
      FILTER cond
      RETURN CONCAT_SEPARATOR(" -- ", INTERLEAVE(p.vertices[*].label, p.edges[*].travelTime))

[
  "London -- 2 -- York -- 3.5 -- Carlisle",
  "London -- 2 -- York -- 4 -- Edinburgh",
  "London -- 2.5 -- Birmingham -- 1 -- Carlisle"
]

Only paths that end at Carlisle or with the last edge having a travel time of over three hours are returned. This excludes the connection to Cologne from the results compared to the previous query.

If you want to exclude the depth at which the prune expression stopped the traversal, you can assign the expression to a variable and use its negated value in a FILTER:

FOR v, e, p IN 2..3 OUTBOUND "places/London" GRAPH "kShortestPathsGraph"
      PRUNE cond = v.label == "Carlisle" OR e.travelTime > 3
      OPTIONS { uniqueVertices: "path" }
      FILTER NOT cond
      RETURN CONCAT_SEPARATOR(" -- ", INTERLEAVE(p.vertices[*].label, p.edges[*].travelTime))

[
  "London -- 2.5 -- Brussels -- 2 -- Cologne"
]

This only returns the connection to Cologne, which is the opposite of the previous example.

You may combine the prune variable with arbitrary other conditions in a FILTER operation. For example, you can remove results where the last edge has as lower travel time than the second to last edge of the path:

FOR v, e, p IN 2..5 OUTBOUND "places/London" GRAPH "kShortestPathsGraph"
      PRUNE cond = v.label == "Carlisle" OR e.travelTime > 3
      OPTIONS { uniqueVertices: "path" }
      FILTER cond AND p.edges[-1].travelTime >= p.edges[-2].travelTime
      RETURN CONCAT_SEPARATOR(" -- ", INTERLEAVE(p.vertices[*].label, p.edges[*].travelTime))

[
  "London -- 2 -- York -- 3.5 -- Carlisle",
  "London -- 2 -- York -- 4 -- Edinburgh"
]

The following examples shows a graph traversal starting at London, with a traversal depth between 2 and 3, and every station is only visited once:

FOR v, e, p IN 2..3 OUTBOUND "places/London" GRAPH "kShortestPathsGraph"
      OPTIONS { uniqueVertices: "path" }
      RETURN CONCAT_SEPARATOR(" -- ", INTERLEAVE(p.vertices[*].label, p.edges[*].travelTime))

[
  "London -- 2.5 -- Brussels -- 2 -- Cologne",
  "London -- 2 -- York -- 3.5 -- Carlisle",
  "London -- 2 -- York -- 3.5 -- Carlisle -- 2 -- Birmingham",
  "London -- 2 -- York -- 3.5 -- Carlisle -- 1 -- Glasgow",
  "London -- 2 -- York -- 4 -- Edinburgh",
  "London -- 2 -- York -- 4 -- Edinburgh -- 1 -- Glasgow",
  "London -- 2 -- York -- 4 -- Edinburgh -- 3 -- Leuchars",
  "London -- 2.5 -- Birmingham -- 1 -- Carlisle",
  "London -- 2.5 -- Birmingham -- 1 -- Carlisle -- 2.5 -- York",
  "London -- 2.5 -- Birmingham -- 1 -- Carlisle -- 1 -- Glasgow"
]

If you add prune conditions to stop the traversal if the station is Glasgow or the travel time less than some number, no results are turned. This is even the case for a value of 2.5, for which two paths exist that fulfill the criterion – to Cologne and Carlisle:

FOR v,e,p IN 2..3 OUTBOUND "places/London" GRAPH "kShortestPathsGraph"
      PRUNE v.label == "Glasgow" OR e.travelTime < 2.5
      OPTIONS { uniqueVertices: "path" }
      RETURN CONCAT_SEPARATOR(" -- ", INTERLEAVE(p.vertices[*].label, p.edges[*].travelTime))

[]

The problem is that null, false, and true are all less than any number (< 2.5) because of AQL’s Type and value order, and because the edge at depth 0 is always null. The prune condition is accidentally fulfilled at the start vertex, stopping the traversal too early. This similarly happens if you check an edge attribute for inequality (!=) and compare it to string, for instance, which evaluates to true for the null value.

The depth at which a traversal is stopped by pruning is considered as a result, but in the above example, the minimum depth of 2 filters the start vertex out. If you lower the minimum depth to 0, you get London as the sole result. This confirms that the traversal stopped at the start vertex.

To avoid this problem, exclude the null value. For example, you can use e.travelTime > 0 AND e.travelTime < 2.5, but more generic solutions are to exclude depth 0 from the check (LENGTH(p.edges) > 0) or to simply ignore the null edge (e != null):

FOR v,e,p IN 2..3 OUTBOUND "places/London" GRAPH "kShortestPathsGraph"
      PRUNE v.label == "Glasgow" OR (e != null AND e.travelTime < 2.5)
      OPTIONS { uniqueVertices: "path" }
      RETURN CONCAT_SEPARATOR(" -- ", INTERLEAVE(p.vertices[*].label, p.edges[*].travelTime))

[
  "London -- 2.5 -- Brussels -- 2 -- Cologne",
  "London -- 2.5 -- Birmingham -- 1 -- Carlisle"
]

Using filters

All three variables emitted by the traversals might as well be used in filter statements. For some of these filter statements the optimizer can detect that it is possible to prune paths of traversals earlier, hence filtered results are not emitted to the variables in the first place. This may significantly improve the performance of your query. Whenever a filter is not fulfilled, the complete set of vertex, edge and path is skipped. All paths with a length greater than the max depth are never computed.

Filter conditions that are AND-combined can be optimized, but OR-combined conditions cannot.

Filtering on paths

Filtering on paths allows for the second most powerful filtering and may have the second highest impact on performance. Using the path variable you can filter on specific iteration depths. You can filter for absolute positions in the path by specifying a positive number (which then qualifies for the optimizations), or relative positions to the end of the path by specifying a negative number.

Filtering edges on the path

This example traversal filters all paths where the start edge (index 0) has the attribute theTruth equal to true. The resulting paths are up to 5 items long:

FOR v, e, p IN 1..5 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
      FILTER p.edges[0].theTruth == true
      RETURN { vertices: p.vertices[*]._key, edges: p.edges[*].label }

[
  {
    "vertices": [
      "A",
      "G"
    ],
    "edges": [
      "right_foo"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "J"
    ],
    "edges": [
      "right_foo",
      "right_zip"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "J",
      "K"
    ],
    "edges": [
      "right_foo",
      "right_zip",
      "right_zup"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "H"
    ],
    "edges": [
      "right_foo",
      "right_blob"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "H",
      "I"
    ],
    "edges": [
      "right_foo",
      "right_blob",
      "right_blub"
    ]
  },
  {
    "vertices": [
      "A",
      "B"
    ],
    "edges": [
      "left_bar"
    ]
  },
  {
    "vertices": [
      "A",
      "B",
      "E"
    ],
    "edges": [
      "left_bar",
      "left_blub"
    ]
  },
  {
    "vertices": [
      "A",
      "B",
      "E",
      "F"
    ],
    "edges": [
      "left_bar",
      "left_blub",
      "left_schubi"
    ]
  },
  {
    "vertices": [
      "A",
      "B",
      "C"
    ],
    "edges": [
      "left_bar",
      "left_blarg"
    ]
  },
  {
    "vertices": [
      "A",
      "B",
      "C",
      "D"
    ],
    "edges": [
      "left_bar",
      "left_blarg",
      "left_blorg"
    ]
  }
]

Filtering vertices on the path

Similar to filtering the edges on the path, you can also filter the vertices:

FOR v, e, p IN 1..5 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
      FILTER p.vertices[1]._key == "G"
      RETURN { vertices: p.vertices[*]._key, edges: p.edges[*].label }

[
  {
    "vertices": [
      "A",
      "G"
    ],
    "edges": [
      "right_foo"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "J"
    ],
    "edges": [
      "right_foo",
      "right_zip"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "J",
      "K"
    ],
    "edges": [
      "right_foo",
      "right_zip",
      "right_zup"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "H"
    ],
    "edges": [
      "right_foo",
      "right_blob"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "H",
      "I"
    ],
    "edges": [
      "right_foo",
      "right_blob",
      "right_blub"
    ]
  }
]

Combining several filters

You can combine filters in any way you like:

FOR v, e, p IN 1..5 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
      FILTER p.edges[0].theTruth == true
         AND p.edges[1].theFalse == false
      FILTER p.vertices[1]._key == "G"
      RETURN { vertices: p.vertices[*]._key, edges: p.edges[*].label }

[
  {
    "vertices": [
      "A",
      "G",
      "J"
    ],
    "edges": [
      "right_foo",
      "right_zip"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "J",
      "K"
    ],
    "edges": [
      "right_foo",
      "right_zip",
      "right_zup"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "H"
    ],
    "edges": [
      "right_foo",
      "right_blob"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "H",
      "I"
    ],
    "edges": [
      "right_foo",
      "right_blob",
      "right_blub"
    ]
  }
]

The query filters all paths where the first edge has the attribute theTruth equal to true, the first vertex is "G" and the second edge has the attribute theFalse equal to false. The resulting paths are up to 5 items long.

Note: Despite the min depth of 1, this only returns results of depth 2. This is because for all results in depth 1, the second edge does not exist and hence cannot fulfill the condition here.

Filter on the entire path

With the help of array comparison operators filters can also be defined on the entire path, like ALL edges should have theTruth == true:

FOR v, e, p IN 1..5 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
      FILTER p.edges[*].theTruth ALL == true
      RETURN { vertices: p.vertices[*]._key, edges: p.edges[*].label }

[
  {
    "vertices": [
      "A",
      "G"
    ],
    "edges": [
      "right_foo"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "J"
    ],
    "edges": [
      "right_foo",
      "right_zip"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "J",
      "K"
    ],
    "edges": [
      "right_foo",
      "right_zip",
      "right_zup"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "H"
    ],
    "edges": [
      "right_foo",
      "right_blob"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "H",
      "I"
    ],
    "edges": [
      "right_foo",
      "right_blob",
      "right_blub"
    ]
  },
  {
    "vertices": [
      "A",
      "B"
    ],
    "edges": [
      "left_bar"
    ]
  },
  {
    "vertices": [
      "A",
      "B",
      "E"
    ],
    "edges": [
      "left_bar",
      "left_blub"
    ]
  },
  {
    "vertices": [
      "A",
      "B",
      "E",
      "F"
    ],
    "edges": [
      "left_bar",
      "left_blub",
      "left_schubi"
    ]
  },
  {
    "vertices": [
      "A",
      "B",
      "C"
    ],
    "edges": [
      "left_bar",
      "left_blarg"
    ]
  },
  {
    "vertices": [
      "A",
      "B",
      "C",
      "D"
    ],
    "edges": [
      "left_bar",
      "left_blarg",
      "left_blorg"
    ]
  }
]

Or NONE of the edges should have theTruth == true:

FOR v, e, p IN 1..5 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
      FILTER p.edges[*].theTruth NONE == true
      RETURN { vertices: p.vertices[*]._key, edges: p.edges[*].label }

[]

Both examples above are recognized by the optimizer and can potentially use other indexes than the edge index.

It is also possible to define that at least one edge on the path has to fulfill the condition:

FOR v, e, p IN 1..5 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
      FILTER p.edges[*].theTruth ANY == true
      RETURN { vertices: p.vertices[*]._key, edges: p.edges[*].label }

[
  {
    "vertices": [
      "A",
      "G"
    ],
    "edges": [
      "right_foo"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "J"
    ],
    "edges": [
      "right_foo",
      "right_zip"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "J",
      "K"
    ],
    "edges": [
      "right_foo",
      "right_zip",
      "right_zup"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "H"
    ],
    "edges": [
      "right_foo",
      "right_blob"
    ]
  },
  {
    "vertices": [
      "A",
      "G",
      "H",
      "I"
    ],
    "edges": [
      "right_foo",
      "right_blob",
      "right_blub"
    ]
  },
  {
    "vertices": [
      "A",
      "B"
    ],
    "edges": [
      "left_bar"
    ]
  },
  {
    "vertices": [
      "A",
      "B",
      "E"
    ],
    "edges": [
      "left_bar",
      "left_blub"
    ]
  },
  {
    "vertices": [
      "A",
      "B",
      "E",
      "F"
    ],
    "edges": [
      "left_bar",
      "left_blub",
      "left_schubi"
    ]
  },
  {
    "vertices": [
      "A",
      "B",
      "C"
    ],
    "edges": [
      "left_bar",
      "left_blarg"
    ]
  },
  {
    "vertices": [
      "A",
      "B",
      "C",
      "D"
    ],
    "edges": [
      "left_bar",
      "left_blarg",
      "left_blorg"
    ]
  }
]

It is guaranteed that at least one, but potentially more edges fulfill the condition. All of the above filters can be defined on vertices in the exact same way.

Filtering on the path vs. filtering on vertices or edges

Filtering on the path influences the Iteration on your graph. If certain conditions aren’t met, the traversal may stop continuing along this path.

In contrast filters on vertex or edge only express whether you’re interested in the actual value of these documents. Thus, it influences the list of returned documents (if you return v or e) similar as specifying a non-null min value. If you specify a min value of 2, the traversal over the first two nodes of these paths has to be executed - you just won’t see them in your result array.

Similar are filters on vertices or edges - the traverser has to walk along these nodes, since you may be interested in documents further down the path.

Examples

Create a simple symmetric traversal demonstration graph:

arangosh> var examples = require("@arangodb/graph-examples/example-graph.js");
arangosh> var graph = examples.loadGraph("traversalGraph");
arangosh> db.circles.toArray();
arangosh> db.edges.toArray();
arangosh> print("once you don't need them anymore, clean them up:");
arangosh> examples.dropGraph("traversalGraph");

[ 
  { 
    "_key" : "A", 
    "_id" : "circles/A", 
    "_rev" : "_fyvMSdi---", 
    "label" : "1" 
  }, 
  { 
    "_key" : "B", 
    "_id" : "circles/B", 
    "_rev" : "_fyvMSdi--_", 
    "label" : "2" 
  }, 
  { 
    "_key" : "C", 
    "_id" : "circles/C", 
    "_rev" : "_fyvMSdm---", 
    "label" : "3" 
  }, 
  { 
    "_key" : "D", 
    "_id" : "circles/D", 
    "_rev" : "_fyvMSdm--_", 
    "label" : "4" 
  }, 
  { 
    "_key" : "E", 
    "_id" : "circles/E", 
    "_rev" : "_fyvMSdm--A", 
    "label" : "5" 
  }, 
  { 
    "_key" : "F", 
    "_id" : "circles/F", 
    "_rev" : "_fyvMSdm--B", 
    "label" : "6" 
  }, 
  { 
    "_key" : "G", 
    "_id" : "circles/G", 
    "_rev" : "_fyvMSdm--C", 
    "label" : "7" 
  }, 
  { 
    "_key" : "H", 
    "_id" : "circles/H", 
    "_rev" : "_fyvMSdq---", 
    "label" : "8" 
  }, 
  { 
    "_key" : "I", 
    "_id" : "circles/I", 
    "_rev" : "_fyvMSdq--_", 
    "label" : "9" 
  }, 
  { 
    "_key" : "J", 
    "_id" : "circles/J", 
    "_rev" : "_fyvMSdq--A", 
    "label" : "10" 
  }, 
  { 
    "_key" : "K", 
    "_id" : "circles/K", 
    "_rev" : "_fyvMSdq--B", 
    "label" : "11" 
  } 
]
[ 
  { 
    "_key" : "63864", 
    "_id" : "edges/63864", 
    "_from" : "circles/A", 
    "_to" : "circles/B", 
    "_rev" : "_fyvMSdu---", 
    "theFalse" : false, 
    "theTruth" : true, 
    "label" : "left_bar" 
  }, 
  { 
    "_key" : "63866", 
    "_id" : "edges/63866", 
    "_from" : "circles/B", 
    "_to" : "circles/C", 
    "_rev" : "_fyvMSdu--_", 
    "theFalse" : false, 
    "theTruth" : true, 
    "label" : "left_blarg" 
  }, 
  { 
    "_key" : "63868", 
    "_id" : "edges/63868", 
    "_from" : "circles/C", 
    "_to" : "circles/D", 
    "_rev" : "_fyvMSdu--A", 
    "theFalse" : false, 
    "theTruth" : true, 
    "label" : "left_blorg" 
  }, 
  { 
    "_key" : "63870", 
    "_id" : "edges/63870", 
    "_from" : "circles/B", 
    "_to" : "circles/E", 
    "_rev" : "_fyvMSdu--B", 
    "theFalse" : false, 
    "theTruth" : true, 
    "label" : "left_blub" 
  }, 
  { 
    "_key" : "63872", 
    "_id" : "edges/63872", 
    "_from" : "circles/E", 
    "_to" : "circles/F", 
    "_rev" : "_fyvMSdy---", 
    "theFalse" : false, 
    "theTruth" : true, 
    "label" : "left_schubi" 
  }, 
  { 
    "_key" : "63874", 
    "_id" : "edges/63874", 
    "_from" : "circles/A", 
    "_to" : "circles/G", 
    "_rev" : "_fyvMSdy--_", 
    "theFalse" : false, 
    "theTruth" : true, 
    "label" : "right_foo" 
  }, 
  { 
    "_key" : "63876", 
    "_id" : "edges/63876", 
    "_from" : "circles/G", 
    "_to" : "circles/H", 
    "_rev" : "_fyvMSdy--A", 
    "theFalse" : false, 
    "theTruth" : true, 
    "label" : "right_blob" 
  }, 
  { 
    "_key" : "63878", 
    "_id" : "edges/63878", 
    "_from" : "circles/H", 
    "_to" : "circles/I", 
    "_rev" : "_fyvMSdy--B", 
    "theFalse" : false, 
    "theTruth" : true, 
    "label" : "right_blub" 
  }, 
  { 
    "_key" : "63880", 
    "_id" : "edges/63880", 
    "_from" : "circles/G", 
    "_to" : "circles/J", 
    "_rev" : "_fyvMSd2---", 
    "theFalse" : false, 
    "theTruth" : true, 
    "label" : "right_zip" 
  }, 
  { 
    "_key" : "63882", 
    "_id" : "edges/63882", 
    "_from" : "circles/J", 
    "_to" : "circles/K", 
    "_rev" : "_fyvMSd2--_", 
    "theFalse" : false, 
    "theTruth" : true, 
    "label" : "right_zup" 
  } 
]
once you don't need them anymore, clean them up:

To get started we select the full graph. For better overview we only return the vertex IDs:

FOR v IN 1..3 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
    RETURN v._key

[
  "G",
  "J",
  "K",
  "H",
  "I",
  "B",
  "E",
  "F",
  "C",
  "D"
]

FOR v IN 1..3 OUTBOUND 'circles/A' edges RETURN v._key

[
  "G",
  "J",
  "K",
  "H",
  "I",
  "B",
  "E",
  "F",
  "C",
  "D"
]

We can nicely see that it is heading for the first outer vertex, then goes back to the branch to descend into the next tree. After that it returns to our start node, to descend again. As we can see both queries return the same result, the first one uses the named graph, the second uses the edge collections directly.

Now we only want the elements of a specific depth (min = max = 2), the ones that are right behind the fork:

FOR v IN 2..2 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
    RETURN v._key

[
  "J",
  "H",
  "E",
  "C"
]

FOR v IN 2 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
    RETURN v._key

[
  "J",
  "H",
  "E",
  "C"
]

As you can see, we can express this in two ways: with or without the max depth parameter.

Filter examples

Now let’s start to add some filters. We want to cut of the branch on the right side of the graph, we may filter in two ways:

• we know the vertex at depth 1 has _key == G
• we know the label attribute of the edge connecting A to G is right_foo

FOR v, e, p IN 1..3 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
      FILTER p.vertices[1]._key != 'G'
      RETURN v._key

[
  "B",
  "E",
  "F",
  "C",
  "D"
]

FOR v, e, p IN 1..3 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
      FILTER p.edges[0].label != 'right_foo'
      RETURN v._key

[
  "B",
  "E",
  "F",
  "C",
  "D"
]

As we can see, all vertices behind G are skipped in both queries. The first filters on the vertex _key, the second on an edge label. Note again, as soon as a filter is not fulfilled for any of the three elements v, e or p, the complete set of these is excluded from the result.

We also may combine several filters, for instance to filter out the right branch (G), and the E branch:

FOR v,e,p IN 1..3 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
      FILTER p.vertices[1]._key != 'G'
      FILTER p.edges[1].label != 'left_blub'
      RETURN v._key

[
  "B",
  "C",
  "D"
]

FOR v,e,p IN 1..3 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
      FILTER p.vertices[1]._key != 'G' AND p.edges[1].label != 'left_blub'
      RETURN v._key

[
  "B",
  "C",
  "D"
]

As you can see, combining two FILTER statements with an AND has the same result.

Comparing OUTBOUND / INBOUND / ANY

All our previous examples traversed the graph in OUTBOUND edge direction. You may however want to also traverse in reverse direction (INBOUND) or both (ANY). Since circles/A only has outbound edges, we start our queries from circles/E:

FOR v IN 1..3 OUTBOUND 'circles/E' GRAPH 'traversalGraph'
      RETURN v._key

[
  "F"
]

FOR v IN 1..3 INBOUND 'circles/E' GRAPH 'traversalGraph'
      RETURN v._key

[
  "B",
  "A"
]

FOR v IN 1..3 ANY 'circles/E' GRAPH 'traversalGraph'
      RETURN v._key

[
  "B",
  "A",
  "G",
  "C",
  "D",
  "F"
]

The first traversal only walks in the forward (OUTBOUND) direction. Therefore from E we only can see F. Walking in reverse direction (INBOUND), we see the path to A: B → A.

Walking in forward and reverse direction (ANY) we can see a more diverse result. First of all, we see the simple paths to F and A. However, these vertices have edges in other directions and they are traversed.

Note: The traverser may use identical edges multiple times. For instance, if it walks from E to F, it continues to walk from F to E using the same edge once again. Due to this, we see duplicate nodes in the result.

Please note that the direction can’t be passed in by a bind parameter.

Use the AQL explainer for optimizations

Now let’s have a look what the optimizer does behind the curtain and inspect traversal queries using the explainer:

FOR v,e,p IN 1..3 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
      LET localScopeVar = RAND() > 0.5
      FILTER p.edges[0].theTruth != localScopeVar
      RETURN v._key

Query String (173 chars, cacheable: false):
   FOR v,e,p IN 1..3 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
       LET localScopeVar = RAND() > 0.5
       FILTER p.edges[0].theTruth != localScopeVar
       RETURN v._key
 

Execution plan:
 Id   NodeType          Est.   Comment
  1   SingletonNode        1   * ROOT
  2   TraversalNode        1     - FOR v  /* vertex (projections: `_key`) */, p  /* paths: edges (projections: `_from`, `_to`, `theTruth`) */ IN 1..3  /* min..maxPathDepth */ OUTBOUND 'circles/A' /* startnode */  GRAPH 'traversalGraph'
  3   CalculationNode      1       - LET localScopeVar = (RAND() > 0.5)   /* simple expression */
  4   CalculationNode      1       - LET #6 = (p.`edges`[0].`theTruth` != localScopeVar)   /* simple expression */
  5   FilterNode           1       - FILTER #6
  6   CalculationNode      1       - LET #8 = v.`_key`   /* attribute expression */
  7   ReturnNode           1       - RETURN #8

Indexes used:
 By   Name   Type   Collection   Unique   Sparse   Cache   Selectivity   Fields        Stored values   Ranges
  2   edge   edge   edges        false    false    false      100.00 %   [ `_from` ]   [  ]            base OUTBOUND

Functions used:
 Name   Deterministic   Cacheable   Uses V8
 RAND   false           false       false  

Traversals on graphs:
 Id  Depth  Vertex collections  Edge collections  Options                                  Filter / Prune Conditions
 2   1..3   circles             edges             uniqueVertices: none, uniqueEdges: path                           

Optimization rules applied:
 Id   RuleName
  1   move-calculations-up
  2   optimize-traversals
  3   remove-redundant-path-var
  4   move-calculations-down

43 rule(s) executed, 1 plan(s) created, peak mem [b]: 0, exec time [s]: 0.00031

FOR v,e,p IN 1..3 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
      FILTER p.edges[0].label == 'right_foo'
      RETURN v._key

Query String (129 chars, cacheable: true):
   FOR v,e,p IN 1..3 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
       FILTER p.edges[0].label == 'right_foo'
       RETURN v._key
 

Execution plan:
 Id   NodeType          Est.   Comment
  1   SingletonNode        1   * ROOT
  2   TraversalNode        1     - FOR v  /* vertex (projections: `_key`) */ IN 1..3  /* min..maxPathDepth */ OUTBOUND 'circles/A' /* startnode */  GRAPH 'traversalGraph'
  5   CalculationNode      1       - LET #7 = v.`_key`   /* attribute expression */
  6   ReturnNode           1       - RETURN #7

Indexes used:
 By   Name   Type   Collection   Unique   Sparse   Cache   Selectivity   Fields        Stored values   Ranges
  2   edge   edge   edges        false    false    false      100.00 %   [ `_from` ]   [  ]            base OUTBOUND
  2   edge   edge   edges        false    false    false      100.00 %   [ `_from` ]   [  ]            level 0 OUTBOUND

Traversals on graphs:
 Id  Depth  Vertex collections  Edge collections  Options                                  Filter / Prune Conditions                   
 2   1..3   circles             edges             uniqueVertices: none, uniqueEdges: path  FILTER (p.`edges`[0].`label` == "right_foo")

Optimization rules applied:
 Id   RuleName
  1   move-calculations-up
  2   move-filters-up
  3   move-calculations-up-2
  4   move-filters-up-2
  5   optimize-traversals
  6   remove-filter-covered-by-traversal
  7   remove-unnecessary-calculations-2
  8   remove-redundant-path-var

44 rule(s) executed, 1 plan(s) created, peak mem [b]: 0, exec time [s]: 0.00028

We now see two queries: In one we add a localScopeVar variable, which is outside the scope of the traversal itself - it is not known inside of the traverser. Therefore, this filter can only be executed after the traversal, which may be undesired in large graphs. The second query on the other hand only operates on the path, and therefore this condition can be used during the execution of the traversal. Paths that are filtered out by this condition won’t be processed at all.

And finally clean it up again:

arangosh> var examples = require("@arangodb/graph-examples/example-graph.js");
arangosh> examples.dropGraph("traversalGraph");

If this traversal is not powerful enough for your needs, like you cannot describe your conditions as AQL filter statements, then you might want to have a look at manually crafted traversers.

Also see how to combine graph traversals.