Overview

Preferential attachment refers to a common phenomenon in complex network that the more connections a node has, the more likely it establishes new connections. If both nodes have a large number of connections, there is great possibility that they will be connected. In 2002, this method is used by A. Barabási and R. Albert in their proposed BA model for producing random scale-free networks:

• R. Albert, A. Barabási, Statistical mechanics of complex networks (2001)

Basic Concept

Preferential Attachment

Preferential attachment measurement uses the product of the number of neighbors of two nodes to determine their closeness, which 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 PA(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 blue node has 3 neighbors, the red node has 4 neighbors, so the score of their preferential attachment is 3 * 4 = 12.

Special Case

Lonely Node, Disconnected Graph

Lonely node does not have any neighbor node, the algorithm does not calculate the Preferential Attachment between lonely node and any other node, either it considers the Preferential Attachment 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 Preferential Attachment between 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 Preferential Attachment of node UUID = 3 and all other nodes, write the algorithm results back to file named pa

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

2. Property Writeback

Not supported by this algorithm.

3. Statistics Writeback

This algorithm has no statistics.

Direct Return

Example: Calculate the Preferential Attachment of node UUID = 3 and UUID = 4, define algorithm results as alias named pa and return the results

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

Streaming Return

Example: Calculate the Preferential Attachment 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: "Preferential_Attachment"
}).stream() as pa 
return pa order by pa.num desc

Real-time Statistics

This algorithm has no statistics.