# 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:

- The vertex on this path.
- 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:

- You start at the vertex
**A**. - 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:

Vertex | Edge |
---|---|

A | null |

B | A → B |

C | B → C |

D | C → 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*): used to modify the execution of the traversal. Only the following attributes have an effect, all others are ignored:**weightAttribute**(string): a top-level edge attribute that should be used to read the edge weight. If the attribute is not existent or not numeric, the*defaultWeight*will be used instead. The attribute value must not be negative.**defaultWeight**(number): this value will be used as fallback if there is no*weightAttribute*in the edge document, or if it is not a number. The value must not be negative. The default is`1`

.

`weightAttribute`

) with a negative value is
encountered during traversal, or if `defaultWeight`

is set to a negative
number, then the query is aborted with an error.### 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.

### 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");
var graph = examples.loadGraph("traversalGraph");
db.circles.toArray();
db.edges.toArray();
```

Start with the shortest path from **A** to **D** as above:

```
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");
```