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AQL graph traversals explained

Traversing a graph means to follow edges connected to a start vertex and neighboring vertices until a specified depth

General query idea

A traversal starts at one specific document (startVertex) and follows all edges connected to this document. For all documents (vertices) that are targeted by these edges it will again follow all edges connected to them and so on. It is possible to define how many of these follow iterations should be executed at least (min depth) and at most (max depth).

For all vertices that were visited during this process in the range between min depth and max depth iterations you will get a result in form of a set with three items:

  1. The visited vertex.
  2. The edge pointing to it.
  3. The complete path from startVertex to the visited vertex as object with an attribute edges and an attribute vertices, each a list of the corresponding elements. These lists are sorted, which means the first element in vertices is the startVertex and the last is the visited vertex, and the n-th element in edges connects the n-th element with the (n+1)-th element in vertices.

Example execution

Let’s take a look at a simple example to explain how it works. This is the graph that we are going to traverse:

traversal graph

We use the following parameters for our query:

  1. We start at the vertex A.
  2. We use a min depth of 1.
  3. We use a max depth of 2.
  4. We follow only in OUTBOUND direction of edges

traversal graph step 1

Now it walks to one of the direct neighbors of A, say B (note: ordering is not guaranteed!):

traversal graph step 2

The query will remember the state (red circle) and will emit the first result A → B (black box). This will also prevent the traverser to be trapped in cycles. Now again it will visit one of the direct neighbors of B, say E:

traversal graph step 3

We have limited the query with a max depth of 2, so it will not pick any neighbor of E, as the path from A to E already requires 2 steps. Instead, we will go back one level to B and continue with any other direct neighbor there:

traversal graph step 4

Again after we produced this result we will step back to B. But there is no neighbor of B left that we have not yet visited. Hence we go another step back to A and continue with any other neighbor there.

traversal graph step 5

And identical to the iterations before we will visit H:

traversal graph step 6

And J:

traversal graph step 7

After these steps there is no further result left. So all together this query has returned the following paths:

  1. A → B
  2. A → B → E
  3. A → B → C
  4. A → G
  5. A → G → H
  6. A → G → J

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