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]]])

Relation inputs

The first positional argument names a registered edge table or view (the edges role). Parenthesized relation subqueries are not accepted; metadata validation uses the same registered name.

Vertex ID types

The edges relation declares the accepted vertex-ID domains. Numeric calls preserve the existing numeric schema. When logical string support is declared, Utf8, LargeUtf8, and Utf8View endpoint columns share one logical domain; their vertex-identity outputs are canonicalized to Utf8.

Domain	Accepted endpoint inputs	Output contract
Numeric edge endpoints	Int32, Int64	The numeric output schema is used for numeric calls.
Logical string edge endpoints	Utf8, LargeUtf8, Utf8View	Vertex identity columns are canonicalized to Utf8; scores, distances, counts, coordinates, and opaque labels remain numeric.

The native mapping type is Int64. Call-specific output schemas come 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

Scalar arguments & JSON 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 schema

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. The full scan, GPU graph build, and count return in about 0.6 s.

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.

Limitations & lifecycle

No algorithm-specific limitations.

Validate before running

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.