Source: https://dev-docs.nebula-graph.io/v5.3.2/analytic/algorithms/closeness_centrality/
Documentation version: v5.3.2

# Closeness Centrality

## Algorithm introduction

Closeness centrality evaluates how near a node is to all other reachable nodes via shortest path distances.

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

For more information, see [Closeness Centrality](https://en.wikipedia.org/wiki/Closeness_centrality).

## Data model

To implement the Closeness 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](https://dev-docs.nebula-graph.io/v5.3.2/analytic/algorithms/closeness_centrality/#1_prepare_graph_data).

## Procedure implementation[]()

To compute Closeness Centrality results, a [procedure](https://dev-docs.nebula-graph.io/v5.3.2/database-gql-reference/procedures/create/) is created.

For more information about the procedure, see [Procedure implementation](https://dev-docs.nebula-graph.io/v5.3.2/analytic/algorithms/closeness_centrality/#procedure_implement). 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](https://dev-docs.nebula-graph.io/v5.3.2/database-gql-reference/variable-definition/value-variable/) | Active set for the current BFS frontier.
 | `source_ids` | Global [SumAgg aggregator value variable](https://dev-docs.nebula-graph.io/v5.3.2/database-gql-reference/variable-definition/agg/sum_agg/) | List of all node IDs used as BFS sources.
 | `has_next` | [Primitive value variable](https://dev-docs.nebula-graph.io/v5.3.2/database-gql-reference/variable-definition/value-variable/) | Whether the BFS frontier has nodes to expand.
 | `vertex_cnt` | Global [SumAgg aggregator value variable](https://dev-docs.nebula-graph.io/v5.3.2/database-gql-reference/variable-definition/agg/sum_agg/) | Total number of nodes in the graph.
 | `dist_sum` | Global [SumAgg aggregator value variable](https://dev-docs.nebula-graph.io/v5.3.2/database-gql-reference/variable-definition/agg/sum_agg/) | Sum of shortest-path distances from the current source.
 | `reach_cnt` | Global [SumAgg aggregator value variable](https://dev-docs.nebula-graph.io/v5.3.2/database-gql-reference/variable-definition/agg/sum_agg/) | Count of nodes reachable from the current source.
 | `inf` | [Primitive value variable](https://dev-docs.nebula-graph.io/v5.3.2/database-gql-reference/variable-definition/value-variable/) | Infinity sentinel for unreachable distances.
 | `source_id` | [Primitive value variable](https://dev-docs.nebula-graph.io/v5.3.2/database-gql-reference/variable-definition/value-variable/) | Current source node ID.
 | `src_idx` | [Primitive value variable](https://dev-docs.nebula-graph.io/v5.3.2/database-gql-reference/variable-definition/value-variable/) | Index into source_ids for outer-loop progress.
 | `level` | [Primitive value variable](https://dev-docs.nebula-graph.io/v5.3.2/database-gql-reference/variable-definition/value-variable/) | Current BFS hop depth.
 | `score` | Node-attached [SumAgg aggregator value variable](https://dev-docs.nebula-graph.io/v5.3.2/database-gql-reference/variable-definition/agg/sum_agg/) | Per-node closeness centrality score.
 | `dist` | Node-attached [SumAgg aggregator value variable](https://dev-docs.nebula-graph.io/v5.3.2/database-gql-reference/variable-definition/agg/sum_agg/) | Per-node shortest-path distance from the current source.
 | `result_table` | [Table variable](https://dev-docs.nebula-graph.io/v5.3.2/database-gql-reference/variable-definition/table-variable/) | Output table storing (vertex_id, score) pairs.

The following steps outline the logic of the procedure:

1. Collect all node IDs into `source_ids` and count `vertex_cnt`.
2. For each source node, run a BFS to compute `dist_sum` (total distances) and `reach_cnt` (reachable nodes).
3. Compute each source node's closeness score as `reach_cnt² / (vertex_cnt × dist_sum)`.
4. Return (`vertex_id`, `score`) for all nodes, sorted by score descending.

## Steps

Run the following code blocks in order in the NebulaGraph Studio CONSOLE. For first-time setup, follow [Prepare algorithm sample data](https://dev-docs.nebula-graph.io/v5.3.2/analytic/algorithms/prepare-data/) to check where to run commands and how the directory is mounted.

### 1. Prepare graph data[]()

1. 

Create a graph type that matches your data model.

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

````

2. 

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

  - [closeness_centrality_node.csv](https://dev-docs.nebula-graph.io/v5.3.2/analytic/algorithms/files/closeness_centrality/closeness_centrality_node.csv): Node data.
  - [closeness_centrality_edge.csv](https://dev-docs.nebula-graph.io/v5.3.2/analytic/algorithms/files/closeness_centrality/closeness_centrality_edge.csv): Edge data.

Preview the CSV files

closeness_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

````

closeness_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

````

3. 

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

````
CREATE TEMPORARY GRAPH IF NOT EXISTS #closeness_centrality_graph TYPED closeness_centrality_graph_type

````

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

````

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

````
'''
USE #closeness_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](https://dev-docs.nebula-graph.io/v5.3.2/analytic/algorithms/prepare-data/#troubleshooting) before continuing.

### 2. Create a procedure[]()

Create a procedure to implement the Closeness Centrality algorithm. For more information about the procedure, see [Procedure implementation](https://dev-docs.nebula-graph.io/v5.3.2/analytic/algorithms/closeness_centrality/#procedure_implement). 

````
'''
CREATE OR REPLACE PROCEDURE closeness_centrality()
RETURNS (vertex_id INT64, score DOUBLE)
COMMENT "Compute classic unweighted closeness centrality for all vertices on an undirected graph, 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 vertex_cnt SumAgg<INT64> = 0
  VALUE dist_sum SumAgg<INT64> = 0
  VALUE reach_cnt SumAgg<INT64> = 0
  VALUE inf INT64 = 1000000000
  VALUE source_id INT64 = 0
  VALUE src_idx INT64 = 0
  VALUE level INT64 = 0

  NODE VALUE score SumAgg<DOUBLE> = 0.0
  NODE VALUE dist MinAgg<INT64> = 1000000000

  TABLE result_table TYPED TABLE {vertex_id INT64, score DOUBLE}

  MATCH (n)
  PER NODE (n) {
    SET n.@score = 0.0
    SET n.@dist = inf
    SET @source_ids += n.id
    SET @vertex_cnt += 1
  }

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

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

    MATCH (s)
    WHERE s.id = source_id
    PER NODE (s) {
      SET s.@dist = 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 {
        MATCH (v)
        WHERE v IN frontier
        PER NODE (v) {
          SET v.@dist = level
          SET @dist_sum += level
          SET @reach_cnt += 1
        }
      }
    }

    MATCH (s)
    WHERE s.id = source_id
    PER NODE (s) {
      IF @dist_sum > 0 AND @reach_cnt = @vertex_cnt - 1 THEN {
        SET s.@score = CAST(@reach_cnt AS DOUBLE) / CAST(@dist_sum AS DOUBLE)
      }
      ELSE {
        SET s.@score = 0.0
      }
    }
  }

  MATCH (n)
  PER NODE (n) {
    EXPORT n.id, n.@score 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 closeness centrality scores for the nodes.

````
USE #closeness_centrality_graph CALL closeness_centrality() RETURN vertex_id, score

````

Returns:

Expand to view results

````
+-----------+---------------------+
| vertex_id | score               |
+-----------+---------------------+
| 14        | 0.4791666666666667  |
| 10        | 0.46938775510204084 |
| 12        | 0.46938775510204084 |
| 15        | 0.4423076923076923  |
| 11        | 0.4339622641509434  |
| 9         | 0.42592592592592593 |
| 16        | 0.42592592592592593 |
| 18        | 0.42592592592592593 |
| 8         | 0.41818181818181815 |
| 13        | 0.41818181818181815 |
| 6         | 0.40350877192982454 |
| 17        | 0.39655172413793105 |
| 19        | 0.3770491803278688  |
| 7         | 0.3709677419354839  |
| 5         | 0.3484848484848485  |
| 4         | 0.34328358208955223 |
| 21        | 0.34328358208955223 |
| 22        | 0.32857142857142857 |
| 2         | 0.3150684931506849  |
| 3         | 0.3150684931506849  |
| 20        | 0.3150684931506849  |
| 1         | 0.27710843373493976 |
| 24        | 0.26744186046511625 |
| 23        | 0.26436781609195403 |
+-----------+---------------------+

````

Save results to a file or graph

To save the returned results as CSV files or write them to a graph, see [EXPORT](https://dev-docs.nebula-graph.io/v5.3.2/database-gql-reference/in-out/export/). Match the exported fields to the returned columns and target properties.