Total Neighbors

Overview

The Total Neighbors algorithm measures the similarity between two nodes by calculating the total number of distinct neighbors they have combined.

Unlike algorithms that focus solely on common neighbors, this method provides a broader perspective by considering the entire neighborhood of both nodes, offering a more comprehensive assessment of their similarity. It is computed using the following formula:

where N(x) and N(y) are the sets of adjacent nodes to nodes x and y respectively.

More total neighbors indicate greater similarity between nodes, while a count of 0 indicates no similarity.

In this example, TN(D,E) = |N(D) ∪ N(E)| = |{B, C, E, F} ∪ {B, D, F}| = |{B, C, D, E, F}| = 5.

Considerations

The Total Neighbors algorithm treats all edges as undirected, ignoring their original direction.

Example Graph

GQL
INSERT (A:default {_id: "A"}), (B:default {_id: "B"}),
       (C:default {_id: "C"}), (D:default {_id: "D"}),
       (E:default {_id: "E"}), (F:default {_id: "F"}),
       (G:default {_id: "G"}), (A)-[:default]->(B),
       (B)-[:default]->(E), (C)-[:default]->(B),
       (C)-[:default]->(D), (C)-[:default]->(F),
       (D)-[:default]->(B), (D)-[:default]->(E),
       (F)-[:default]->(D)

Parameters

Name	Type	Default	Description
`node1`	`STRING`	/	Required. First node `_id`.
`node2`	`STRING`	/	Required. Second node `_id`.

Run Mode

Returns:

Column	Type	Description
`node1`	`STRING`	First node identifier (`_id`)
`node2`	`STRING`	Second node identifier (`_id`)
`score`	`FLOAT`	Total neighbors count (union of neighborhoods)

GQL
CALL algo.totalneighbors({
  node1: "C",
  node2: "E"
}) YIELD node1, node2, score

Result:

node1	node2	score
C	E	3

Stream Mode

Returns the same columns as run mode, streamed for memory efficiency.

GQL
CALL algo.totalneighbors.stream({
  node1: "C",
  node2: "E"
}) YIELD node1, node2, score
RETURN node1, node2, score

Result:

node1	node2	score
C	E	3

Stats Mode

Returns:

Column	Type	Description
`score`	`FLOAT`	Total neighbors score

GQL
CALL algo.totalneighbors.stats({
  node1: "C",
  node2: "E"
}) YIELD score

Result:

score
3