K-Hop

Algorithm introduction

K-hop traversal enumerates nodes reachable within at most K edges from a source node.

Return the deduplicated exact k-hop reachable nodes from source_id in a directed graph whose node primary key is id. Nodes reached within fewer than k hops are excluded.

For more information, see K-Hop.

Data model

To implement the K-Hop 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 K-Hop 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:

• source_id: INT64. ID of the source node to expand from.
• k: INT64. Maximum number of hops from the source node.

Additionally, the following variables are defined within the procedure:

Variable name	Variable type	Description
frontier	Primitive value variable	Active set of nodes in the current hop layer.
step	Primitive value variable	Current hop count from the source node.
has_next	Primitive value variable	Whether the current frontier expanded to new nodes.
result_ids	Global SumAgg aggregator value variable	Accumulated list of visited node IDs across all hops.
visited	Node-attached SumAgg aggregator value variable	Per-node flag: node has been reached.

The following steps outline the logic of the procedure:

1. Initialize the source node as visited; add it to result_ids and set it as the initial frontier.
2. For each hop step up to k, expand the frontier: find all unvisited neighbors, mark them visited, add to result_ids, and set as the new frontier.
3. Stop when has_next is false (no new nodes reached) or step equals k.
4. Return the list of all visited node IDs within k hops.

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 k_hop_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/k_hop/ under your deployment directory:

   • k_hop_node.csv: Node data.
   • k_hop_edge.csv: Edge data.
   Preview the CSV files

   k_hop_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
   

   k_hop_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 #k_hop_graph TYPED k_hop_graph_type
   

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

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

   '''
   USE #k_hop_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 K-Hop algorithm. For more information about the procedure, see Procedure implementation.

'''
CREATE OR REPLACE PROCEDURE k_hop(source_id INT64, k INT64)
RETURNS (vertex_ids LIST<INT64>)
COMMENT "Return the deduplicated exact k-hop reachable vertices from source_id in a directed graph whose vertex primary key is id. Vertices reached within fewer than k hops are excluded."
AS {
  VALUE frontier ACTIVE_SET

  VALUE step INT64 = 0
  VALUE has_next OrAgg = false
  VALUE result_ids ListAgg<INT64>

  NODE VALUE visited OrAgg = false

  MATCH (s)
  WHERE s.id = source_id
  PER NODE (s) {
    SET s.@visited = true
  }
  FINALLY {
    SET frontier = s
  }

  WHILE step < k THEN {
    SET @has_next = false
    SET step = step + 1

    MATCH (s)-[e]->(t)
    WHERE s IN frontier AND t.@visited = false
    PER PATH {
      SET t.@visited += true
      SET @has_next += true
    }
    FINALLY {
      SET frontier = t
    }

    IF @has_next = false THEN {
      BREAK
    }
  }

  IF step = k THEN {
    MATCH (n)
    WHERE n IN frontier
    PER NODE (n) {
      SET @result_ids += n.id
    }
  }

  RETURN @result_ids AS vertex_ids
}
'''

3. Call your procedure

Expand from node 1 and return the IDs visited within at most 2 hops.

USE #k_hop_graph CALL k_hop(1, 2) RETURN vertex_ids

Returns:

+--------------+
| vertex_ids   |
+--------------+
| [7, 8, 9, 6] |
+--------------+

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.