Triangle Count All
UDTF: cugraph_triangle_count_all
Official cuGraph reference: C API
Count the number of three-vertex cycles incident to every vertex in the graph.
Quickstart
The call below supplies edges from registered relation target_edges with canonical src and dst columns and may include weight. Substitute your own registered relations.
SELECT *
FROM cugraph_triangle_count_all(
edges => (SELECT src, dst FROM target_edges)
);
Inputs
Every relation is a named parenthesized SELECT subquery. The required edges role uses canonical src and dst columns; every role, its canonical columns, and their accepted Arrow types are listed under Relation arguments. Metadata validation resolves registered tables named in its JSON request.
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
Relation arguments
Every edge_id column must have the integer type of src and dst; string-keyed graphs accept no edge IDs.
Named value arguments
This UDTF has no algorithm-specific value arguments. Its inputs are the relation arguments above and the graph construction options below.
Graph construction options
This UDTF requires directed=false (undirected/symmetric graph); all other graph construction options follow the shared defaults documented in Graph Construction Options.
Output
These are generic descriptor schemas; run gpu_validate_call to get the concrete, table-specific output schema.
Examples
These examples run on the citation network demo dataset.
Which well-connected papers have the tightest citation neighborhoods?
Treating citation edges as undirected, triangle_count gives the triangles
touching each paper. The local clustering coefficient 2T / (d·(d−1))
divides that count by the possible pairs among its neighbors. This query ranks
papers with at least 200 undirected neighbors by the share of those pairs that
are connected in the same graph:
WITH tri AS (
SELECT vertex, triangle_count
FROM cugraph_triangle_count_all(edges => (SELECT src, dst FROM citation_edges))),
deg AS (
SELECT vertex, in_degree AS degree
FROM cugraph_degrees_all(
edges => (SELECT src, dst FROM citation_edges), 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;
The top rows have coefficients from 0.117 to 0.146, meaning 11.7% to 14.6% of possible neighbor pairs are connected. SIFT has 46 times as many triangles as the top row but a coefficient near 0.0005 because its 22,925 neighbors create far more possible pairs.
Limits
No algorithm-specific limitations.
To dry-run validate relation metadata, column types, and options without execution, see gpu_validate_call.