Betweenness Centrality¶

Algorithm introduction¶

Betweenness centrality quantifies how often a node lies on shortest paths between other node pairs.

Compute classic unweighted betweenness centrality for all nodes on an undirected graph via the Brandes algorithm, using node property id as the identifier and treating shortest paths by hop count.

For more information, see Betweenness Centrality.

Data model¶

To implement the Betweenness Centrality algorithm in GQL, the following data model is used to create a graph type:

Entities are represented by nodes of type Node, with properties id and rating.
Relationships are represented by edges of type Link, with property weight.

For the complete definition of the graph type, see Prepare graph data.

Procedure implementation ¶

To compute Betweenness Centrality results, a procedure is created.

For more information about the procedure, see Procedure implementation. The following section describes the key components of the procedure and how it works.

The procedure takes the following input parameters:

This procedure does not require input parameters.

Additionally, the following variables are defined within the procedure:

Variable name	Variable type	Description
`frontier`	Primitive value variable	Active set holding the current BFS frontier nodes.
`source_ids`	Global SumAgg aggregator value variable	List of all node IDs used as BFS sources.
`has_next`	Primitive value variable	Whether the BFS frontier is non-empty for the current source.
`inf`	Primitive value variable	Infinity sentinel for uninitialized distances.
`source_id`	Primitive value variable	Current source node ID in the outer BFS loop.
`src_idx`	Primitive value variable	Index into source_ids for outer-loop progress.
`level`	Primitive value variable	Current BFS hop depth from the active source.
`max_level`	Primitive value variable	Maximum BFS depth reached for the current source.
`rev_level`	Primitive value variable	Reverse traversal level during back-propagation.
`bc`	Node-attached SumAgg aggregator value variable	Per-node accumulated betweenness centrality score.
`dist`	Node-attached SumAgg aggregator value variable	Per-node shortest-path hop distance from the current source.
`sigma`	Node-attached SumAgg aggregator value variable	Per-node count of shortest paths from the current source.
`delta`	Node-attached SumAgg aggregator value variable	Per-node dependency score accumulated during back-propagation.
`result_table`	Table variable	Output table storing (vertex_id, score) pairs.

The following steps outline the logic of the procedure:

Collect all node IDs into source_ids and initialize per-node dist, sigma, and delta.
For each source node, run a BFS to compute shortest-path hop counts (dist) and path counts (sigma).
Back-propagate dependency scores (delta) from the deepest BFS level back to the source, accumulating each node's contribution into bc.
Return each node's accumulated betweenness score (vertex_id, score), sorted descending.

Steps¶

Run the following code blocks in order in the NebulaGraph Studio CONSOLE. For first-time setup, follow Prepare algorithm sample data to check where to run commands and how the directory is mounted.

1. Prepare graph data ¶

Create a graph type that matches your data model.

'''
CREATE GRAPH TYPE IF NOT EXISTS betweenness_centrality_graph_type AS {
    NODE Node (LABEL Node {id INT PRIMARY KEY, rating INT}),
    EDGE Link (Node)-[LABEL Link {weight INT, MULTIEDGE KEY()}]->(Node)
}
'''

Download these CSV files and save them with their original names in examples/algorithms/betweenness_centrality/ under your deployment directory:

betweenness_centrality_node.csv: Node data.
betweenness_centrality_edge.csv: Edge data.

Preview the CSV files

betweenness_centrality_node.csv

id,rating
1,0
2,2
3,1
4,0
5,0
6,2
7,1
8,2
9,0
10,1
11,0
12,2
13,1
14,1
15,0
16,2
17,0
18,1
19,2
20,0
21,2
22,1
23,0
24,1

betweenness_centrality_edge.csv

src_id,dst_id,weight
1,2,4
1,3,2
1,4,7
1,5,9
2,3,1
2,4,6
2,5,5
2,6,2
3,4,3
3,5,4
3,6,8
4,6,2
4,7,6
4,8,5
5,6,4
5,8,7
5,9,6
6,8,1
6,9,5
6,10,6
7,9,2
7,10,9
8,9,3
8,11,6
8,12,4
9,10,4
9,12,7
9,13,2
10,12,1
10,13,8
10,14,4
11,12,2
11,14,5
11,15,7
12,14,3
12,15,6
12,16,5
13,15,2
13,16,7
14,15,4
14,17,8
14,18,2
15,16,1
15,18,5
15,19,3
16,18,3
16,19,6
17,18,2
17,20,7
17,21,5
18,19,4
18,21,9
18,22,6
19,21,1
19,22,5
20,21,3
20,23,6
20,24,8
21,22,2
21,23,4
21,24,7
22,24,4
23,24,1

Create a temporary graph based on the graph type and load the data files into the temporary graph.

CREATE TEMPORARY GRAPH IF NOT EXISTS #betweenness_centrality_graph TYPED betweenness_centrality_graph_type

'''
USE #betweenness_centrality_graph IMPORT INTO GRAPH {
      NODE (v@Node {id: id, rating: rating}) FROM DATAFILE {
          PATH: "file:///examples/algorithms/betweenness_centrality/betweenness_centrality_node.csv",
          FORMAT: "CSV",
          DELIMITER: ','
      },
      EDGE (id: src_id)-[e@Link {weight: weight}]->(id: dst_id) FROM DATAFILE {
          PATH: "file:///examples/algorithms/betweenness_centrality/betweenness_centrality_edge.csv",
          FORMAT: "CSV",
          DELIMITER: ','
      }
  }
'''

After the import succeeds, run this query in the console to check the node count:

'''
USE #betweenness_centrality_graph
MATCH (n)
RETURN count(n) AS node_count
'''

The expected node_count is 24. If it differs, check the files and import results before continuing.

2. Create a procedure ¶

Create a procedure to implement the Betweenness Centrality algorithm. For more information about the procedure, see Procedure implementation.

'''
CREATE OR REPLACE PROCEDURE betweenness_centrality()
RETURNS (vertex_id INT64, score DOUBLE)
COMMENT "Compute classic unweighted betweenness centrality for all vertices on an undirected graph via the Brandes algorithm, using vertex property id as the identifier and treating shortest paths by hop count."
AS {
  VALUE frontier ACTIVE_SET

  VALUE source_ids ListAgg<INT64>
  VALUE has_next OrAgg = false
  VALUE inf INT64 = 1000000000
  VALUE source_id INT64 = 0
  VALUE src_idx INT64 = 0
  VALUE level INT64 = 0
  VALUE max_level INT64 = 0
  VALUE rev_level INT64 = 0

  NODE VALUE bc SumAgg<DOUBLE> = 0.0
  NODE VALUE dist MinAgg<INT64> = 1000000000
  NODE VALUE sigma SumAgg<DOUBLE> = 0.0
  NODE VALUE delta SumAgg<DOUBLE> = 0.0

  TABLE result_table TYPED TABLE {vertex_id INT64, score DOUBLE}

  MATCH (n)
  PER NODE (n) {
    SET n.@bc = 0.0
    SET @source_ids += n.id
  }

  WHILE src_idx < @source_ids.size() THEN {
    SET source_id = @source_ids[src_idx]
    SET src_idx = src_idx + 1
    SET level = 0
    SET max_level = 0

    MATCH (n)
    PER NODE (n) {
      SET n.@dist = inf
      SET n.@sigma = 0.0
      SET n.@delta = 0.0
    }

    MATCH (s)
    WHERE s.id = source_id
    PER NODE (s) {
      SET s.@dist = 0
      SET s.@sigma = 1.0
      SET s.@delta = 0.0
    }
    FINALLY {
      SET frontier = s
    }

    SET @has_next = true

    WHILE @has_next = true THEN {
      SET @has_next = false
      SET level = level + 1

      MATCH (u)-[e]-(v)
      WHERE u IN frontier AND v.@dist = inf
      PER PATH {
        SET @has_next += true
      }
      FINALLY {
        SET frontier = v
      }

      IF @has_next = true THEN {
        SET max_level = level

        MATCH (v)
        WHERE v IN frontier
        PER NODE (v) {
          SET v.@dist = level
        }

        MATCH (v)-[e]-(u)
        WHERE v IN frontier AND u.@dist = level - 1
        PER PATH {
          SET v.@sigma += u.@sigma
        }
      }
    }

    SET rev_level = max_level

    WHILE rev_level > 0 THEN {
      MATCH (v)-[e]-(w)
      WHERE v.@dist = rev_level - 1 AND w.@dist = rev_level
      PER PATH {
        VALUE contrib DOUBLE = 0.0

        IF w.@sigma > 0.0 THEN {
          SET contrib = (v.@sigma / w.@sigma) * (1.0 + w.@delta)
          SET v.@delta += contrib
        }
      }

      MATCH (w)
      WHERE w.@dist = rev_level AND w.id <> source_id
      PER NODE (w) {
        SET w.@bc += w.@delta
      }

      SET rev_level = rev_level - 1
    }
  }

  MATCH (n)
  PER NODE (n) {
    EXPORT n.id, n.@bc / 2.0 INTO result_table
  }

  FOR r IN result_table
  RETURN r.vertex_id AS vertex_id, r.score AS score
  ORDER BY score DESC, vertex_id ASC
}
'''

3. Call your procedure ¶

Compute betweenness centrality scores for the nodes.

USE #betweenness_centrality_graph CALL betweenness_centrality() RETURN vertex_id, score

Returns:

Expand to view results

+-----------+--------------------+
| vertex_id | score              |
+-----------+--------------------+
| 14        | 67.8918657967101   |
| 10        | 51.75309772968774  |
| 18        | 40.30392916544371  |
| 12        | 37.370764716983835 |
| 6         | 33.38757193543222  |
| 8         | 32.13354984875291  |
| 17        | 30.42103303694065  |
| 21        | 29.912102529148715 |
| 15        | 26.875354636179623 |
| 9         | 24.913164244339967 |
| 5         | 16.162075382607817 |
| 16        | 15.65169579580913  |
| 19        | 14.87225072961119  |
| 11        | 12.14105197018898  |
| 4         | 12.043896472711737 |
| 13        | 11.120121682305985 |
| 22        | 6.730357142857143  |
| 20        | 6.524206994660801  |
| 7         | 3.3496843489235455 |
| 2         | 1.1211129203521168 |
| 3         | 1.1211129203521168 |
| 24        | 1.0                |
| 1         | 0.2                |
| 23        | 0.0                |
+-----------+--------------------+

Save results to a file or graph

To save the returned results as CSV files or write them to a graph, see EXPORT. Match the exported fields to the returned columns and target properties.

Betweenness Centrality¶

Algorithm introduction¶

Data model¶

Procedure implementation¶

Steps¶

1. Prepare graph data¶

2. Create a procedure¶

3. Call your procedure¶

Procedure implementation ¶

1. Prepare graph data ¶

2. Create a procedure ¶

3. Call your procedure ¶