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

Run the following statements on an empty graph to define its structure and insert data:

GQLUQL
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),
       (F)-[:default]->(G);

Creating HDC Graph

To load the entire graph to the HDC server hdc-server-1 as my_hdc_graph:

GQLUQL
CREATE HDC GRAPH my_hdc_graph ON "hdc-server-1" OPTIONS {
  nodes: {"*": ["*"]},
  edges: {"*": ["*"]},
  direction: "undirected",
  load_id: true,
  update: "static"
}

Parameters

Algorithm name: topological_link_prediction

File Writeback

GQLUQL
CALL algo.topological_link_prediction.write("my_hdc_graph", {
  ids: ["C"],
  ids2: ["A","E","G"],
  type: "Total_Neighbors",
  return_id_uuid: "id"
}, {
  file: {
    filename: "tn"
  }
})

Result:

File: tn
_id1,_id2,result
C,A,3
C,E,3
C,G,3

Full Return

GQLUQL
CALL algo.topological_link_prediction.run("my_hdc_graph", {
  ids: ["C"],
  ids2: ["A","C","E","G"],
  type: "Total_Neighbors",
  return_id_uuid: "id"
}) YIELD tn
RETURN tn

Result:

Stream Return

GQLUQL
CALL algo.topological_link_prediction.stream("my_hdc_graph", {
  ids: ["C"],
  ids2: ["A", "B", "D", "E", "F", "G"],
  type: "Total_Neighbors",
  return_id_uuid: "id"
}) YIELD tn
FILTER tn.result >= 4
RETURN tn

Result: