K-Hop Fast

Overview

The K-Hop Fast algorithm counts the number of nodes reachable within a specified hop range from a given start node. It uses a bitmap-based BFS with direction-optimized traversal, designed for high performance on large graphs.

Concepts

K-Hop Neighbors

The K-hop neighbors of a node are the nodes located at a shortest distance of K from that node. The shortest distance is the number of edges in the shortest path. In graph theory, a hop is when a node travels to another node via an edge.

In this graph, nodes {B, C, D} are the 1-hop neighbors of node A, {E, F, G} are the 2-hop neighbors, and {H} is the 3-hop neighbor.

Key properties of K-hop neighbors:

K is determined solely by the shortest distance and is unique. For example, there may be many paths between two nodes, but K is always the shortest. A node will only appear at one hop level.
K-hop results are deduplicated. Even if multiple shortest paths exist to the same node, it appears only once.

Considerations

This algorithm requires the compute engine topology. Run ALTER GRAPH <graphName> SET COMPUTE ENABLED before using it.

Example Graph

GQL
INSERT (card1:card {_id: "card1"}), (card2:card {_id: "card2"}),
       (card3:card {_id: "card3"}), (card4:card {_id: "card4"}),
       (card5:card {_id: "card5"}), (card6:card {_id: "card6"}),
       (card7:card {_id: "card7"}), (card8:card {_id: "card8"}),
       (card1)-[:transfer]->(card2), (card2)-[:transfer]->(card3),
       (card2)-[:transfer]->(card7), (card2)-[:transfer]->(card7),
       (card3)-[:transfer]->(card4), (card4)-[:transfer]->(card3),
       (card5)-[:transfer]->(card2), (card6)-[:transfer]->(card2),
       (card7)-[:transfer]->(card3), (card8)-[:transfer]->(card3)

Parameters

Name	Type	Default	Description
`startNode`	`STRING`	/	Required. Starting node `_id`.
`maxHops`	`INT`	`3`	Maximum number of hops.
`minHops`	`INT`	`1`	Minimum number of hops to start counting.
`direction`	`STRING`	`out`	Edge direction: `in`, `out`, or `both`.

Run Mode

Returns:

Column	Type	Description
`count`	`INT`	Total number of K-hop neighbors in the hop range
`hops`	`LIST`	Per-hop counts as a list of integers

GQL
CALL algo.khop_fast({
  startNode: "card1",
  maxHops: 3,
  direction: "out"
}) YIELD count, hops

Result:

count	hops
1	4

Stats Mode

Returns:

Column	Type	Description
`count`	`INT`	Total number of K-hop neighbors
`nodeCount`	`INT`	Total nodes in graph

GQL
CALL algo.khop_fast.stats({
  startNode: "card1",
  maxHops: 3,
  direction: "out"
}) YIELD count, nodeCount

Result:

count	nodeCount
3	8