Leiden

SQL function: cugraph_leiden

Official cuGraph reference: C API

Find modularity-based communities with refinement steps that improve the internal connectedness of the partitions.

Signature

cugraph_leiden(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_leiden('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

Option	Type	Default	Constraints	Description
`max_level`	`UInt32`	`100`	min 1	Maximum number of hierarchy levels (coarsening rounds) to run. Lowering it truncates the hierarchy earlier.
`resolution`	`Float64`	`1`	> 0	Resolution parameter (gamma) in the modularity formula. Higher values produce more, smaller communities; lower values produce fewer, larger ones.
`seed`	`UInt64`	`0`		Seed for the native random-number generator state that drives the randomized refinement phase. Different seeds explore different refinements.
`theta`	`Float64`	`1`	> 0	Scales the modularity gain in the Leiden refinement phase when computing the probability of joining a random community. Larger values make refinement more random.

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 assigned to a Leiden community.
`partition`	`Int64`	no	Community identifier assigned by Leiden.

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

Examples

This example runs on the citation network demo dataset.

Where Leiden disagrees with Louvain

Leiden takes the same call shape as cugraph_louvain but adds a refinement phase that guarantees well-connected communities, splitting clusters Louvain merges. Joining the two partitions on vertex shows exactly where. The views are the Louvain example's 2010s AI subgraph:

CREATE OR REPLACE VIEW ai_nodes AS
SELECT paper_id FROM papers
WHERE year >= 2010 AND primary_fos IN (
  'Deep learning', 'Artificial neural network', 'Convolutional neural network',
  'Recurrent neural network', 'Natural language processing',
  'Reinforcement learning', 'Image segmentation', 'Feature extraction',
  'Object detection', 'Speech recognition');

CREATE OR REPLACE VIEW ai_edges AS
SELECT e.src, e.dst
FROM citation_edges e
JOIN ai_nodes a ON a.paper_id = e.src
JOIN ai_nodes b ON b.paper_id = e.dst;

WITH lv AS (
  SELECT vertex, "partition" AS louvain_c FROM cugraph_louvain('ai_edges', 'src', 'dst')),
ld AS (
  SELECT vertex, "partition" AS leiden_c FROM cugraph_leiden('ai_edges', 'src', 'dst')),
joint AS (
  SELECT lv.louvain_c, ld.leiden_c, COUNT(*) AS n
  FROM lv JOIN ld ON ld.vertex = lv.vertex
  GROUP BY lv.louvain_c, ld.leiden_c)
SELECT louvain_c,
       SUM(n) AS members,
       COUNT(*) FILTER (WHERE n >= 50) AS leiden_parts
FROM joint
GROUP BY louvain_c
HAVING SUM(n) > 2500
ORDER BY leiden_parts DESC, members DESC;

louvain_c	members	leiden_parts
0	10,684	8
1	6,707	7
3	5,118	3
2	3,960	3

Louvain's 10,684-paper computer-vision community shatters into eight Leiden communities of 50+ members; overall the same graph yields 1,960 Louvain communities versus 2,670 for Leiden. When a Louvain community is only held together by a few incidental citations, Leiden's refinement phase is what separates it — the guarantee that every returned community is internally connected is the reason to prefer Leiden as the default. Both runs are deterministic here (seed defaults to 0), which is why the community ids in this table are stable across sessions.

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_leiden',
  '{"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.

Signature​

Quickstart​

Inputs​

Arguments and options​

Positional scalar arguments​

JSON options​

Graph construction options​

Output​

Examples​

Where Leiden disagrees with Louvain​

Limits​

Validate the call​