# 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

```
[WITH vertexCollection1[, vertexCollection2[, ...vertexCollectionN]]]
FOR vertex[, edge[, path]]
IN [min[..max]]
OUTBOUND|INBOUND|ANY startVertex
GRAPH graphName
[OPTIONS options]
```

`WITH`

: optional for single server instances, but required for graph traversals in a cluster.**collections**(collection,*repeatable*): list of vertex collections that will be involved in the traversal

`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 will start at the traversal depth of*min*(thus edges and vertices below will not be 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*can not be specified without*min*.

`OUTBOUND|INBOUND|ANY`

: follow outgoing, incoming, or edges pointing in either direction in the traversal; Please note that this can’t be replaced by a bind parameter.**startVertex**(string|object): a vertex where the traversal will originate from. This can be specified in the form of an ID string or in the form of a document with the attribute`_id`

. All other values will 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 will be looked up. Note that the graph name is like a regular string, hence it must be enclosed by quote marks.`OPTIONS`

**options**(object,*optional*): used to modify the execution of the traversal. Only the following attributes have an effect, all others are ignored:**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).**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. - “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 will follow cycles in edges.

**bfs**(bool): optionally use the alternative breadth-first traversal algorithm- true – the traversal will be executed breadth-first. The results will first contain all vertices at depth 1. Than all vertices at depth 2 and so on.
- false (default) – the traversal will be executed depth-first. It will first
return all paths from
*min*depth to*max*depth for one vertex at depth 1. Than for the next vertex at depth 1 and so on.

### Working with collection sets

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

Instead of `GRAPH graphName`

you may specify a list of edge collections. Vertex
collections are determined by the edges in the edge collections. The traversal
options are the same as with the named graph variant.

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

### 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 will 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’s not possible to predict which will be visited in a traversal. Hence, which collections need to be locked can only be determined at run time. Deadlocks may occur under certain circumstances.

Please consider to use the `WITH`

statement to
specify the collections you expect to be involved.

## Using filters and the explainer to extrapolate the costs

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 will
not be 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* will be skipped. All paths
with a length greater than *max* will never be computed.

In the current state, `AND`

combined filters can be optimized, but `OR`

combined filters cannot.

### Filtering on paths

Filtering on paths allows for the most powerful filtering and may have the 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

```
FOR v, e, p IN 1..5 OUTBOUND 'circles/A' GRAPH 'traversalGraph'
FILTER p.edges[0].theTruth == true
RETURN p
```

will filter all paths where the start edge (index 0) has the attribute
*theTruth* equal to *true*. The resulting paths will be up to 5 items long.

### 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 p
```

#### Combining several filters

And of course you can combine these 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 p
```

The query will filter 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 will be up to
5 items long.

**Note**: Although we have defined a *min* of 1, we will only get 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 p
```

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 p
```

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 p
```

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 interestet 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

We will create a simple symmetric traversal demonstration graph:

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

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:

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

### 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`

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 will be excluded from the result.

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

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`

:

The first traversal will only walk 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 will be traversed.

**Note**: The traverser may use identical edges multiple times. For instance,
if it walks from **E** to **F**, it will continue to walk from **F** to **E**
using the same edge once again. Due to this we will 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:

We now see two queries: In one we add a variable *localScopeVar*, 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.