Total Neighbors

Overview

The Total Neighbors algorithm computes the total number of distinct neighbors of two nodes as a measure of their similarity.

This algorithm takes into account the entire neighborhood of both nodes, giving a more comprehensive view of their similarity compared to algorithms that only focus on common neighbors. 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 number of 0 indicates no similarity between two nodes.

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 ignores the direction of edges but calculates them as undirected edges.

Syntax

• Command: algo(topological_link_prediction)
• Parameters:

Example

The example graph is as follows:

File Writeback

UQL
algo(topological_link_prediction).params({
  uuids: [3],
  uuids2: [1,5,7],
  type: 'Total_Neighbors'
}).write({
  file:{ 
    filename: 'tn'
  }
})

Results: File tn

File
C,A,3.000000
C,E,3.000000
C,G,3.000000

Direct Return

UQL
algo(topological_link_prediction).params({
  ids: 'C',
  ids2: ['A','C','E','G'],
  type: 'Total_Neighbors'
}) as tn 
return tn 

Results: tn

Stream Return

UQL
find().nodes() as n
with collect(n._id) as nID
algo(topological_link_prediction).params({
  ids: 'C',
  ids2: nID,
  type: 'Total_Neighbors'
}).stream() as tn
where tn.num >= 4
return tn

Results: tn