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v4.0
    v4.0

    Common Neighbors

    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

    node1 node2 num
    3 1 1
    3 2 1
    3 4 2
    3 5 2
    3 6 1
    3 7 1

    Algorithm statistics: N/A

    Command and Configuration

    • Command: algo(topological_link_prediction)
    • Configurations for the parameter params():
    Name
    Type
    Default
    Specification Description
    ids / uuids []_id / []_uuid / Mandatory IDs or UUIDs of the first set of nodes to be calculated, only need to configure one of them; every node in ids/uuids will be paired with every node in ids2/uuids2 for calculation
    ids2 / uuids2 []_id / []_uuid / Mandatory IDs or UUIDs of the second set of nodes to be calculated, only need to configure one of them; every node in ids/uuids will be paired with every node in ids2/uuids2 for calculation
    type string Adamic_Adar Adamic_Adar / Common_Neighbors / Preferential_Attachment / Resource_Allocation / Total_Neighbors Measurement of the closeness of the node pair; Adamic_Adar means to calculate AA index, Common_Neighbors means to calculate the number of common neighbors, Preferential_Attachment means to calculate the score of preferential attachment, Resource_Allocation means to calculate the score of resource allocation, Total_Neighbors means to calculate the number of total neighbors
    limit int -1 >=-1 Number of results to return; return all results if sets to -1 or not set

    Algorithm Execution

    Task Writeback

    1. File Writeback

    Configuration Data in Each Row
    filename node1,node2,num

    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

    Alias Ordinal Type
    Description
    Column Name
    0 []perNodePair Closeness of node pair node1, node2, num

    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

    Alias Ordinal Type
    Description
    Column Name
    0 []perNodePair Closeness of node pair node1, node2, num

    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.

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