# Shortest Path in AQL

With the shortest path algorithm, you can find one shortest path between two vertices using AQL

## General query idea

This type of query is supposed to find the shortest path between two given documents (startVertex and targetVertex) in your graph. For all vertices on this shortest path you will get a result in form of a set with two items:

1. The vertex on this path.
2. The edge pointing to it.

### Example execution

Let’s take a look at a simple example to explain how it works. This is the graph that you are going to find a shortest path on:

You can use the following parameters for the query:

1. You start at the vertex A.
2. You finish with the vertex D.

So, obviously, you have the vertices A, B, C and D on the shortest path in exactly this order. Then, the shortest path statement returns the following pairs:

VertexEdge
Anull
BA → B
CB → C
DC → D

Note that the first edge is always `null` because there is no edge pointing to the startVertex.

## Syntax

The next step is to see how you can write a shortest path query. You have two options here, you can either use a named graph or a set of edge collections (anonymous graph).

### Working with named graphs

``````FOR vertex[, edge]
IN OUTBOUND|INBOUND|ANY SHORTEST_PATH
startVertex TO targetVertex
GRAPH graphName
[OPTIONS options]``````
• `FOR`: Emits up to two variables:
• vertex (object): The current vertex on the shortest path
• edge (object, optional): The edge pointing to the vertex
• `IN` `OUTBOUND|INBOUND|ANY`: Defines in which direction edges are followed (outgoing, incoming, or both)
• startVertex `TO` targetVertex (both string|object): The two vertices between which the shortest path will be computed. 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 one of the specified documents 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.
• `OPTIONS` options (object, optional): See the path search options.

### Working with collection sets

``````FOR vertex[, edge]
IN OUTBOUND|INBOUND|ANY SHORTEST_PATH
startVertex TO targetVertex
edgeCollection1, ..., edgeCollectionN
[OPTIONS options]``````

Instead of `GRAPH graphName` you may specify a list of edge collections (anonymous graph). The involved vertex collections are determined by the edges of the given edge collections. The rest of the behavior is similar to the named version.

### Path search options

You can optionally specify the following options to modify the execution of a graph path search. If you specify unknown options, query warnings are raised.

#### `weightAttribute`

A top-level edge attribute that should be used to read the edge weight (string).

If the attribute does not exist or is not numeric, the `defaultWeight` is used instead.

The attribute value must not be negative.

#### `defaultWeight`

This value is used as fallback if there is no `weightAttribute` in the edge document, or if it’s not a number (number).

The value must not be negative. The default is `1`.

#### `useCache`

Introduced in: v3.12.2

Whether to use the in-memory cache for edges. The default is `true`.

You can set this option to `false` to not make a large graph operation pollute the edge cache.

### Traversing in mixed directions

For shortest path 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 search direction and `ANY` specifically for edges2 as follows:

``````FOR vertex IN OUTBOUND SHORTEST_PATH
startVertex TO targetVertex
edges1, ANY edges2, edges3``````

All collections in the list that do not specify their own direction will use the direction defined after `IN` (here: `OUTBOUND`). This allows to use a different direction for each collection in your path search.

## Conditional shortest path

The `SHORTEST_PATH` computation only finds an unconditioned shortest path. With this construct it is not possible to define a condition like: “Find the shortest path where all edges are of type X”. If you want to do this, use a normal Traversal instead with the option `{order: "bfs"}` in combination with `LIMIT 1`.

Please also consider using `WITH` to specify the collections you expect to be involved.

## Examples

Creating a simple symmetric traversal demonstration graph:

``````var examples = require("@arangodb/graph-examples/example-graph");
db.circles.toArray();
db.edges.toArray();``````

``````db._query(`
FOR v, e IN OUTBOUND SHORTEST_PATH 'circles/A' TO 'circles/D' GRAPH 'traversalGraph'
RETURN [v._key, e._key]
`);

db._query(`
FOR v, e IN OUTBOUND SHORTEST_PATH 'circles/A' TO 'circles/D' edges
RETURN [v._key, e._key]
`);``````

You can see that expectations are fulfilled. You find the vertices in the correct ordering and the first edge is null, because no edge is pointing to the start vertex on this path.

You can also compute shortest paths based on documents found in collections:

``````db._query(`
FOR a IN circles
FILTER a._key == 'A'
FOR d IN circles
FILTER d._key == 'D'
FOR v, e IN OUTBOUND SHORTEST_PATH a TO d GRAPH 'traversalGraph'
RETURN [v._key, e._key]
`);

db._query(`
FOR a IN circles
FILTER a._key == 'A'
FOR d IN circles
FILTER d._key == 'D'
FOR v, e IN OUTBOUND SHORTEST_PATH a TO d edges
RETURN [v._key, e._key]
`);``````

And finally clean it up again:

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