Overview

Common neighbors refer to the common adjacent nodes to both nodes. The number of common neighbors of two nodes can be used to describe the closeness of them.

Basic Concept

Common Neighbors

The number of common neighbors is calculated by the following formula:

where N(x) and N(y) are neighbor sets of x and y respectively. The larger the value of CN(x,y) is, the closer the two nodes are, value of 0 indicates that the two nodes are not close.

Taking the above graph as an example, the common neighbors of the blue and red nodes are the yellow and green 2 nodes.

Special Case

Lonely Node, Disconnected Graph

Lonely node does not have any neighbor node, the algorithm does not calculate the common neighbors between lonely node and any other node, either it considers the common neighbors of two nodes which are located in different connected components.

Self-loop Edge

The algorithm ignores all self-loop edges when calculating neighbor nodes.

Directed Edge

For directed edges, the algorithm ignores the direction of edges but calculates them as undirected edges.

Results and Statistics

Take the graph below as an example, run the algorithm in the graph:

Algorithm results: Calculate the number of common neighbors of node 3 and other nodes, return node1, node2 and num

Algorithm statistics: N/A

Command and Configuration

• Command: algo(topological_link_prediction)
• Configurations for the parameter params():

Algorithm Execution

Task Writeback

1. File Writeback

Example: Calculate the number of common neighbors of node UUID = 3 and all other nodes, write the algorithm results back to file named cn

algo(topological_link_prediction).params({
  uuids: [3],
  uuids2: [1,2,4,5,6,7],
  type: "Common_Neighbors"
  }).write({
  file:{ 
    filename: "cn"
  }
})

2. Property Writeback

Not supported by this algorithm.

3. Statistics Writeback

This algorithm has no statistics.

Direct Return

Example: Calculate the number of common neighbors of node UUID = 3 and UUID = 4, define algorithm results as alias named number and return the results

algo(topological_link_prediction).params({
  uuids: [3],
  uuids2: [4],
  type: "Common_Neighbors"
}) as number 
return number

Streaming Return

Example: Calculate the number of common neighbors of node UUID = 1 and UUID = 5,6,7, return the results in the descending closeness score

algo(topological_link_prediction).params({
  uuids: [1],
  uuids2: [5,6,7],
  type: "Common_Neighbors"
}).stream() as cn 
return cn order by cn.num desc

Real-time Statistics

This algorithm has no statistics.