PageRank

SQL function: cugraph_pagerank

Official cuGraph reference: C API

Rank vertices by the stationary probability of a damped random walk that follows outgoing edges.

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_pagerank(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

Argument	Required	Columns	Description
edges	yes	src, dst: Int32, Int64, Utf8, LargeUtf8, Utf8View weight (optional): Float32, Float64 edge_id (optional): Int32, Int64	edge relation with canonical src and dst columns, plus optional weight and edge_id columns

Every edge_id column must have the integer type of src and dst; string-keyed graphs accept no edge IDs.

Named value arguments

Option	Type	Default	Constraints	Description
alpha	number	0.85	min 0; max 1	PageRank damping factor in [0, 1]
epsilon	number	0.00001	> 0	positive convergence tolerance
max_iterations	integer	100	min 1; max 4294967295	maximum iteration count, at least 1

Graph construction options

Graph construction follows the shared defaults (directed=true, renumbering, python_cugraph policy) documented in Graph Construction Options.

Output

Column	Type	Nullable	Description
vertex	Int64|Utf8	no	Vertex receiving the PageRank score.
value	Float64	no	PageRank score for the vertex.

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 (4.9M papers, 45.6M src-cites-dst edges).

PageRank versus raw citation counts

PageRank over the full graph, joined back to paper metadata. Importance flows through citations, so a paper's score depends on who cites it, not only on how many do; on this dataset that lets papers with modest raw counts rank above papers with more, but shallower, citations.

SELECT p.title, p.year, p.n_citation, r.value AS pagerank
FROM cugraph_pagerank(edges => (SELECT src, dst FROM citation_edges)) r
JOIN papers p ON p.paper_id = r.vertex
ORDER BY r.value DESC
LIMIT 5;

title	year	n_citation	pagerank
Finite automata and their decision problems	1959	1,401	0.00139
The Mathematical Theory of Communication	1949	48,327	0.00134
The reduction of two-way automata to one-way automata	1959	224	0.00126
The complexity of theorem-proving procedures	1971	4,592	0.00073
A mathematical theory of communication	1948	22,122	0.00066

In this run the first and third papers have modest raw counts (1,401 and 224 citations), but the papers citing them are themselves foundational results, and PageRank propagates that structure. The full call (45.6M edges, GPU graph build, 4.1M scores, join, and sort) returned in about 1.5 s on the capture host; that is an observation from one run, not a performance figure.

Window functions over the result

The output of a cugraph_* function is a plain relation, so ROW_NUMBER() applies directly to it. This query finds where the paper that introduced PageRank ranks, by its own algorithm, among 4.9 million papers. The corpus holds two 1998 records with this title (the WWW conference paper and a journal record with two in-corpus citations), so the filter also pins venue.

WITH ranked AS (
  SELECT vertex, value, ROW_NUMBER() OVER (ORDER BY value DESC) AS rank
  FROM cugraph_pagerank(edges => (SELECT src, dst FROM citation_edges)))
SELECT r.rank, p.title, p.year, r.value
FROM ranked r JOIN papers p ON p.paper_id = r.vertex
WHERE p.title = 'The anatomy of a large-scale hypertextual Web search engine'
  AND p.year = 1998 AND p.venue = 'The Web Conference';

rank	title	year	value
115	The anatomy of a large-scale hypertextual Web search engine	1998	0.000143

Rank #115 of 4,894,081 in this run.

SQL defines which graph the GPU sees

The named edges relation can read any table or view. Joining the edge list to papers on both endpoints restricts the graph to citations within a chosen era, and PageRank then ranks the most important papers within that window (here, the pre-2000 literature).

CREATE OR REPLACE VIEW edges_pre2000 AS
SELECT e.src, e.dst
FROM citation_edges e
JOIN papers ps ON ps.paper_id = e.src
JOIN papers pd ON pd.paper_id = e.dst
WHERE ps.year BETWEEN 1901 AND 2000 AND pd.year BETWEEN 1901 AND 2000;

SELECT p.year, p.title
FROM cugraph_pagerank(edges => (SELECT src, dst FROM edges_pre2000)) r
JOIN papers p ON p.paper_id = r.vertex
ORDER BY r.value DESC
LIMIT 6;

year	title
1959	Finite automata and their decision problems
1959	The reduction of two-way automata to one-way automata
1949	The Mathematical Theory of Communication
1974	The Design and Analysis of Computer Algorithms
1958	Preliminary report: international algebraic language
1963	Machine perception of three-dimensional solids

Automata theory, information theory, the classic algorithms textbook, and the ALGOL report: the view's WHERE clause restricts the graph to one era, and the algorithm re-ranks the field within it.

Limits

No algorithm-specific limitations.

To dry-run validate relation metadata, column types, and options without execution, see gpu_validate_call.