Triangle Count

Algorithm introduction

Triangle count computes the number of closed triplets in the graph and can be used to estimate clustering strength.

Count the number of undirected triangles in a graph whose node primary key is id.

For more information, see Triangle Count.

Data model

To implement the Triangle Count 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 Triangle Count 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
total	Global SumAgg aggregator value variable	Global accumulator for the total triangle count.
fwd	Node-attached SumAgg aggregator value variable	Per-node set of neighbor IDs with a larger ID (used for triangle intersection).

The following steps outline the logic of the procedure:

1. For each edge (s, t) where s.id < t.id, add t.id to s's fwd neighbor set.
2. For each edge (s, t) where s.id < t.id, check each node u in t's fwd set; if u is also in s's fwd set, increment total.
3. Each common entry represents a closed triangle; the count is divided by 1 (already deduplicated by the ID ordering).
4. Return the total triangle count.

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

1. Create a graph type that matches your data model.

   '''
   CREATE GRAPH TYPE IF NOT EXISTS triangle_count_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/triangle_count/ under your deployment directory:

   • triangle_count_node.csv: Node data.
   • triangle_count_edge.csv: Edge data.
   Preview the CSV files

   triangle_count_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
   

   triangle_count_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 #triangle_count_graph TYPED triangle_count_graph_type
   

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

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

   '''
   USE #triangle_count_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 Triangle Count algorithm. For more information about the procedure, see Procedure implementation.

'''
CREATE OR REPLACE PROCEDURE triangle_count()
RETURNS (triangle_count INT64)
COMMENT "Count the number of undirected triangles in a graph whose vertex primary key is id."
AS {
  VALUE total SumAgg<INT64> = 0

  NODE VALUE fwd SetAgg<INT64>

  MATCH (s)-[e]-(t)
  WHERE s.id < t.id
  PER PATH {
    SET s.@fwd += t.id
  }

  MATCH (s)-[e]-(t)
  WHERE s.id < t.id
  PER PATH {
    VALUE idx INT64 = 0
    VALUE candidate_id INT64 = 0

    WHILE idx < t.@fwd.size() THEN {
      SET candidate_id = t.@fwd[idx]
      IF s.@fwd.contains_key(candidate_id) THEN {
        SET @total += 1
      }
      SET idx = idx + 1
    }
  }

  RETURN @total AS triangle_count
}
'''

3. Call your procedure

Count the triangles in the sample graph.

USE #triangle_count_graph CALL triangle_count() RETURN triangle_count

Returns:

+----------------+
| triangle_count |
+----------------+
| 47             |
+----------------+

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.