Triangle Count

Overview

The Triangle Count algorithm identifies and counts triangles in a graph, where each triangle consists of three mutually connected nodes. Triangles indicate the presence of loops and strong connectivity patterns, making them important for graph structure analysis.

In social networks, triangles indicate cohesive communities. In financial or transaction networks, triangles may signal suspicious or fraudulent behavior.

Concepts

Triangle

A triangle is formed by three nodes that are all connected to each other. The graph below contains 2 triangles: {a, b, c} and {b, c, d}.

The algorithm counts the number of triangles each node participates in and also computes the local clustering coefficient as a byproduct.

Considerations

The algorithm treats all edges as undirected.
Triangles are counted by nodes — multi-edges between the same pair of nodes are deduplicated and counted as a single connection.

Example Graph

GQL
INSERT (C1:default {_id: "C1"}), (C2:default {_id: "C2"}),
       (C3:default {_id: "C3"}), (C4:default {_id: "C4"}),
       (C5:default {_id: "C5"}), (C6:default {_id: "C6"}),
       (C4)-[:default]->(C1), (C4)-[:default]->(C1),
       (C4)-[:default]->(C2), (C1)-[:default]->(C2),
       (C2)-[:default]->(C3), (C1)-[:default]->(C3),
       (C3)-[:default]->(C5), (C3)-[:default]->(C6)

Parameters

Name	Type	Default	Description
`limit`	`INT`	`-1`	Limits the number of results returned (-1 = all).
`order`	`STRING`	/	Sorts the results by `triangleCount`: `asc` or `desc`.

Run Mode

Returns:

Column	Type	Description
`nodeId`	`STRING`	Node identifier (`_id`)
`triangleCount`	`INT`	Number of triangles the node participates in
`coefficient`	`FLOAT`	Local clustering coefficient

GQL
CALL algo.trianglecount({
  order: "desc"
}) YIELD nodeId, triangleCount, coefficient

Result:

nodeId	triangleCount	coefficient
C2	2	0.6666666666666666
C1	2	0.6666666666666666
C3	1	0.16666666666666666
C4	1	1
C6	0	0
C5	0	0

Stream Mode

Returns the same columns as run mode, streamed for memory efficiency.

GQL
CALL algo.trianglecount.stream() YIELD nodeId, triangleCount
FILTER triangleCount > 0
RETURN nodeId, triangleCount

Result:

nodeId	triangleCount
C2	2
C3	1
C1	2
C4	1

Stats Mode

Returns:

Column	Type	Description
`nodeCount`	`INT`	Total number of nodes
`totalTriangles`	`INT`	Total number of unique triangles in the graph
`avgCoefficient`	`FLOAT`	Average clustering coefficient

GQL
CALL algo.trianglecount.stats() YIELD nodeCount, totalTriangles, avgCoefficient

Result:

nodeCount	totalTriangles	avgCoefficient
6	2	0.4166666666666667

Write Mode

Computes results and writes them back to node properties. The write configuration is passed as a second argument map.

Write parameters:

Name	Type	Description
`db.property`	`STRING` or `MAP`	Node property to write results to. String: writes the `triangleCount` column in results to a property. Map: explicit column-to-property mapping (e.g., `{triangleCount: 'tri_count', coefficient: 'lcc'}`).

Writable columns:

Column	Type	Description
`triangleCount`	`INT`	Triangle count
`coefficient`	`FLOAT`	Local clustering coefficient

Returns:

Column	Type	Description
`task_id`	`STRING`	Task identifier for tracking via `SHOW TASKS`
`nodesWritten`	`INT`	Number of nodes with properties written
`computeTimeMs`	`INT`	Time spent computing the algorithm (milliseconds)
`writeTimeMs`	`INT`	Time spent writing properties to storage (milliseconds)

GQL
CALL algo.trianglecount.write({}, {
  db: {
    property: "tri_count"
  }
}) YIELD task_id, nodesWritten, computeTimeMs, writeTimeMs