Eigenvector Centrality

SQL function: 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.

Signature

cugraph_eigenvector_centrality(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_eigenvector_centrality('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
epsilon	Float64	0.000001	> 0	Power-iteration convergence tolerance: iteration stops once the L1 norm of the score change between consecutive iterations drops below epsilon. Smaller values tighten convergence and may need more iterations.
max_iterations	UInt32	200	min 1	Upper bound on power iterations. The call fails with a non-convergence error if the bound is reached before epsilon is met.

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 eigenvector centrality score.
value	Float64	no	Eigenvector centrality score for 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.

The recursive core of the literature

Eigenvector centrality has no damping and no teleport: a paper scores highly only if the papers citing it score highly themselves. On 45.6M citation edges the fixed point concentrates all mass in the most self-reinforcing corner of the graph — the 1970s theory and databases canon:

SELECT p.title, p.year, ROUND(e.value, 3) AS eigenvector
FROM cugraph_eigenvector_centrality('citation_edges', 'src', 'dst') e
JOIN papers p ON p.paper_id = e.vertex
ORDER BY e.value DESC
LIMIT 6;

title	year	eigenvector
A relational model of data for large shared data banks	1970	0.351
The Design and Analysis of Computer Algorithms	1974	0.244
The complexity of theorem-proving procedures	1971	0.171
Further Normalization of the Data Base Relational Model	1972	0.153
New Directions in Cryptography	1976	0.146
Reducibility Among Combinatorial Problems	2010	0.129

The relational data model, the classic algorithms textbook, the founding NP-completeness results, and the paper that introduced public-key cryptography (the 2010 year on the last row is a reprint edition in the corpus). Compare with the PageRank example, whose damping spreads importance much further out.

Quantify the winner-take-all behavior

Both functions return plain relations, so one statement can measure how much more concentrated eigenvector mass is than PageRank mass — here, the top 100 of 4.1M scored papers hold 10.7% of all eigenvector centrality but only 2.8% of all PageRank:

WITH eig AS (
  SELECT value, ROW_NUMBER() OVER (ORDER BY value DESC) AS rn
  FROM cugraph_eigenvector_centrality('citation_edges', 'src', 'dst')),
pr AS (
  SELECT value, ROW_NUMBER() OVER (ORDER BY value DESC) AS rn
  FROM cugraph_pagerank('citation_edges', 'src', 'dst'))
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;

eigenvector_top100_pct	pagerank_top100_pct
10.7	2.8

If a ranking should reward being cited by the canon, this concentration is the point; if it should surface important work across eras and fields, prefer PageRank or Katz.

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_eigenvector_centrality',
  '{"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.