Eigenvector Centrality
UDTF: cugraph_eigenvector_centrality
Official cuGraph reference: C API
Score vertices by connections to other high-scoring vertices, using power iteration to find the dominant eigenvector.
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_eigenvector_centrality(
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
Graph construction options
Graph construction follows the shared defaults (directed=true, renumbering, python_cugraph policy) 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 papers sit at the center of the citation network's self-reinforcing core?
This ranking gives more weight to papers cited by other high-scoring papers. Its ordering can differ from a ranking by raw citation counts because each incoming citation contributes according to the citing paper's score.
SELECT p.title, p.year, ROUND(e.value, 3) AS eigenvector
FROM cugraph_eigenvector_centrality(edges => (SELECT src, dst FROM citation_edges)) e
JOIN papers p ON p.paper_id = e.vertex
ORDER BY e.value DESC
LIMIT 6;
The displayed papers span database systems, algorithms, cryptography, and combinatorial problems. The 2010 year for Reducibility Among Combinatorial Problems is the reprint edition recorded in this corpus. PageRank returns a different score distribution, as shown in the comparison below.
Would a reading list based on these scores concentrate on a few papers?
Comparing the top 100 scores with the sum of all returned scores shows how concentrated each ranking is. This measures score distribution, not the quality or coverage of the papers in a reading list.
WITH eig AS (
SELECT value, ROW_NUMBER() OVER (ORDER BY value DESC) AS rn
FROM cugraph_eigenvector_centrality(edges => (SELECT src, dst FROM citation_edges))),
pr AS (
SELECT value, ROW_NUMBER() OVER (ORDER BY value DESC) AS rn
FROM cugraph_pagerank(edges => (SELECT src, dst FROM citation_edges)))
SELECT
ROUND(100.0 * (SELECT SUM(value) FROM eig WHERE rn <= 100)
/ (SELECT SUM(value) FROM eig), 1) AS eigenvector_top100_pct,
ROUND(100.0 * (SELECT SUM(value) FROM pr WHERE rn <= 100)
/ (SELECT SUM(value) FROM pr), 1) AS pagerank_top100_pct;
In this run, the top 100 account for 10.7% of the sum of eigenvector scores, compared with 2.8% of the sum of PageRank scores. A larger share describes a more concentrated score distribution; it does not establish that those papers are higher quality.
Limits
No algorithm-specific limitations.
To dry-run validate relation metadata, column types, and options without execution, see gpu_validate_call.