[[search-aggregations-bucket-adjacency-matrix-aggregation]]
=== Adjacency Matrix Aggregation

A bucket aggregation returning a form of https://en.wikipedia.org/wiki/Adjacency_matrix[adjacency matrix].
The request provides a collection of named filter expressions, similar to the `filters` aggregation
request. 
Each bucket in the response represents a non-empty cell in the matrix of intersecting filters.

Given filters named `A`, `B` and `C` the response would return buckets with the following names:


[options="header"]
|=======================
|  h|A   h|B  h|C   
h|A |A   |A&B |A&C 
h|B |    |B   |B&C 
h|C |    |    |C  
|=======================

The intersecting buckets e.g `A&C` are labelled using a combination of the two filter names separated by
the ampersand character. Note that the response does not also include a "C&A" bucket as this would be the
same set of documents as "A&C". The matrix is said to be _symmetric_ so we only return half of it. To do this we sort 
the filter name strings and always use the lowest of a pair as the value to the left of the "&" separator. 

An alternative `separator` parameter can be passed in the request if clients wish to use a separator string 
other than the default of the ampersand.


Example:

[source,js]
--------------------------------------------------
PUT /emails/_bulk?refresh
{ "index" : { "_id" : 1 } }
{ "accounts" : ["hillary", "sidney"]}
{ "index" : { "_id" : 2 } }
{ "accounts" : ["hillary", "donald"]}
{ "index" : { "_id" : 3 } }
{ "accounts" : ["vladimir", "donald"]}

GET emails/_search
{
  "size": 0,
  "aggs" : {
    "interactions" : {
      "adjacency_matrix" : {
        "filters" : {
          "grpA" : { "terms" : { "accounts" : ["hillary", "sidney"] }},
          "grpB" : { "terms" : { "accounts" : ["donald", "mitt"] }},
          "grpC" : { "terms" : { "accounts" : ["vladimir", "nigel"] }}
        }
      }
    }
  }
}
--------------------------------------------------
// CONSOLE

In the above example, we analyse email messages to see which groups of individuals 
have exchanged messages.
We will get counts for each group individually and also a count of messages for pairs
of groups that have recorded interactions.

Response:

[source,js]
--------------------------------------------------
{
  "took": 9,
  "timed_out": false,
  "_shards": ...,
  "hits": ...,
  "aggregations": {
    "interactions": {
      "buckets": [
        {
          "key":"grpA",
          "doc_count": 2
        },
        {
          "key":"grpA&grpB",
          "doc_count": 1
        },
        {
          "key":"grpB",
          "doc_count": 2
        },
        {
          "key":"grpB&grpC",
          "doc_count": 1
        },
        {
          "key":"grpC",
          "doc_count": 1
        }
      ]
    }
  }
}
--------------------------------------------------
// TESTRESPONSE[s/"took": 9/"took": $body.took/]
// TESTRESPONSE[s/"_shards": \.\.\./"_shards": $body._shards/]
// TESTRESPONSE[s/"hits": \.\.\./"hits": $body.hits/]

==== Usage
On its own this aggregation can provide all of the data required to create an undirected weighted graph.
However, when used with child aggregations such as a `date_histogram` the results can provide the
additional levels of data required to perform https://en.wikipedia.org/wiki/Dynamic_network_analysis[dynamic network analysis]
where examining interactions _over time_ becomes important.

==== Limitations
For N filters the matrix of buckets produced can be N²/2 and so there is a default maximum 
imposed of 100 filters . This setting can be changed using the `index.max_adjacency_matrix_filters` index-level setting.