Edge Betweenness Centrality

SQL function: cugraph_edge_betweenness_centrality

Official cuGraph reference: C API

Measure how often each edge lies on shortest paths between vertex pairs, exactly or from an explicit sample of source vertices.

Signature

cugraph_edge_betweenness_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_edge_betweenness_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
exact_vertex_threshold	UInt64	100000		Maximum actual graph vertex count allowed for exact betweenness without explicit seeds or k.
k	UInt64|null	null	min 1; mutually exclusive with seeds	Deterministic approximate seed count. Execution uses the first k distinct graph vertices in stable order and refuses k larger than the actual vertex count.
normalized	Boolean	true		When true, scores are scaled by the maximum possible value for the vertex count and directedness so results lie in [0, 1]; when false, raw shortest-path counts are returned.
seeds	List<Int64>|List<Utf8>|null	null	mutually exclusive with k	Explicit homogeneous integer or string seed vertices for approximate betweenness. Null requests exact all-vertex betweenness unless k is set.

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
source	Int64|Utf8	no	Algorithm result column.
destination	Int64|Utf8	no	Algorithm result column.
score	Float64	no	Algorithm result column.

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.

The citations that bridge subfields

Where vertex betweenness scores papers, edge betweenness scores individual citations. The output is one row per edge (source, destination, score), so joining papers twice labels both ends of each load-bearing link. The graph is the same ~38k-vertex 2010s AI subgraph used by the Louvain and betweenness examples:

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;

SELECT ps.title AS citing, pd.title AS cited, ROUND(b.score, 5) AS edge_betweenness
FROM cugraph_edge_betweenness_centrality('ai_edges', 'src', 'dst') b
JOIN papers ps ON ps.paper_id = b.source
JOIN papers pd ON pd.paper_id = b.destination
ORDER BY b.score DESC
LIMIT 5;

citing	cited	edge_betweenness
Rich Feature Hierarchies for Accurate Object Detection and Semantic Segmentation	Regionlets for Generic Object Detection	0.00022
Squeeze-and-Excitation Networks	Regularized Evolution for Image Classifier Architecture Search	0.00021
Improving object detection with deep convolutional networks via Bayesian optimization and structured prediction	Deep learning in neural networks	0.00017
SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size	Shallow Networks for High-Accuracy Road Object-Detection	0.00016
A survey on deep learning in medical image analysis	Deep Learning Convolutional Networks for Multiphoton Microscopy Vasculature Segmentation.	0.00014

The pattern is the classic edge-betweenness signature: the top links are not famous-cites-famous, they are the single citations that connect a hub (R-CNN, SENet, SqueezeNet, a survey) to an otherwise peripheral cluster — the bridge a whole niche crosses to reach the rest of the field. Exact edge betweenness touches every source–edge pair, so this call is much heavier than its vertex counterpart: in this run it took about 1.5 minutes on this subgraph, versus under a second for vertex betweenness on the capture host. The same exact_vertex_threshold / k / seeds policy applies on larger graphs.

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_edge_betweenness_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.