Triangle Count All

SQL function: cugraph_triangle_count_all

Official cuGraph reference: C API

Count the number of three-vertex cycles incident to every vertex in the graph.

Signature

cugraph_triangle_count_all(table_name [, src_col, dst_col [, weight_col [, options_json]]])

Quickstart

The call below expects a registered edge table or view target_edges with endpoint columns src and dst. Substitute your own registered relations.

SELECT * FROM cugraph_triangle_count_all('target_edges');

Inputs

table_name must be a registered edge table or view (the edges role); parenthesized subqueries are not accepted, and metadata validation resolves the same registered name.

Endpoint columns accept numeric Int32, Int64 vertex IDs or logical string Utf8, LargeUtf8, Utf8View vertex IDs; string vertex-identity outputs are canonicalized to Utf8 (native mapping Int64) while scores, distances, counts, coordinates, and opaque labels stay numeric. The shared vertex-ID contract is summarized in Vertex ID support; the concrete call-specific schema comes from gpu_validate_call.

Logical string side-input limitations:

• edge ID columns and edge-ID predicate side inputs are not supported for logical string graphs

Arguments and options

Positional scalar arguments

src_col and dst_col name the edge endpoint columns; both are optional and default to src and dst.

Argument	Type	Required	Default	Notes
weight_col	Utf8|null	no		accepted as an edge-column binding; native algorithm execution does not consume weights; semantic effect: none for this algorithm

JSON options

This function has no algorithm-specific options.

Graph construction options

This function builds an undirected graph by default (directed=false); all other graph construction options follow the shared defaults documented in Graph Construction Options.

Output

Column	Type	Nullable	Description
vertex	Int64|Utf8	no	Vertex whose triangle participation is reported.
triangle_count	Int64	no	Number of triangles incident to the vertex.

These are generic descriptor schemas; validate the call to get the concrete, table-specific output schema.

Examples

These examples run on the citation network demo dataset.

Count every triangle in 45.6M edges

A triangle in a citation graph is a paper that cites two works which also cite each other — the unit of tightly interlinked literature. One call counts them for every vertex (edges are treated as undirected):

SELECT COUNT(*) AS vertices,
       SUM(triangle_count) AS triangle_sum,
       MAX(triangle_count) AS max_triangles
FROM cugraph_triangle_count_all('citation_edges', 'src', 'dst');

vertices	triangle_sum	max_triangles
4,146,772	202,557,720	143,168

SUM counts each triangle once per corner, so the graph holds ~67.5M distinct triangles; the busiest single paper (the SIFT paper, Distinctive Image Features from Scale-Invariant Keypoints) sits on 143,168 of them. In this run the full scan, GPU graph build, and count returned in about 0.6 s on the capture host.

Local clustering coefficient in plain SQL

Raw triangle counts track degree. Normalizing by the possible neighbor pairs — the local clustering coefficient 2T / (d·(d−1)) — separates communities from hubs. With {"directed": false} the in_degree column of cugraph_degrees_all is exactly the triangle graph's neighbor count, so two GPU calls joined in SQL give the coefficient:

WITH tri AS (
  SELECT vertex, triangle_count
  FROM cugraph_triangle_count_all('citation_edges', 'src', 'dst')),
deg AS (
  SELECT vertex, in_degree AS degree
  FROM cugraph_degrees_all('citation_edges', 'src', 'dst', NULL,
                           '{"directed": false}'))
SELECT p.title, p.year, d.degree, t.triangle_count,
       ROUND(2.0 * t.triangle_count / (d.degree * (d.degree - 1)), 3) AS clustering
FROM tri t
JOIN deg d ON d.vertex = t.vertex
JOIN papers p ON p.paper_id = t.vertex
WHERE d.degree >= 200
ORDER BY clustering DESC
LIMIT 5;

title	year	degree	triangle_count	clustering
Out of Control: Overcoming Control-Flow Integrity	2014	208	3,134	0.146
Discriminative Correlation Filter with Channel and Spatial Reliability	2017	211	2,687	0.121
Signature Schemes with Bounded Leakage Resilience	2009	200	2,380	0.120
Smashing the Gadgets: Hindering Return-Oriented Programming Using In-place Code Randomization	2012	201	2,407	0.120
A Leakage-Resilient Mode of Operation	2009	210	2,566	0.117

Among well-connected papers (degree ≥ 200), the most clustered neighborhoods are systems-security and leakage-resilient-crypto papers — communities where everyone cites everyone. The contrast with a hub: SIFT has 46× the triangles of the top row but a coefficient of just 0.0005, because its 22,925 neighbors barely know each other.

Limits

No algorithm-specific limitations.

Validate the call

Dry-run validation checks registered relation metadata, column presence, static dtypes, and options only; it does not scan edge data, construct a graph, or prove source-vertex existence:

SELECT * FROM gpu_validate_call(
  'cugraph_triangle_count_all',
  '{"schema_version":1,"relations":{"edges":{"table":"target_edges"}},"options":{"src_col":"src","dst_col":"dst"}}'
);

See GPU Function Catalog API for the full gpu_validate_call contract.