✓ File Writeback ✕ Property Writeback ✓ Direct Return ✓ Stream Return ✕ Stats

Overview

Jaccard similarity, or Jaccard index, was proposed by Paul Jaccard in 1901. It’s a metric of similarity for two sets of data. In the graph, collecting the neighbors of a node into a set, two nodes are considered similar if their neighbor sets are similar.

Jaccard similarity ranges from 0 to 1; 1 means that two sets are exactly the same, 0 means that the two sets do not have any element in common.

Concepts

Jaccard Similarity

Given two sets A and B, the Jaccard similarity between them is computed as:

In the following example, set A = {b,c,e,f,g}, set B = {a,d,b,g}, their intersection A⋂B = {b,g}, their union A⋃B = {a,b,c,d,e,f,g}, hence the Jaccard similarity between A and B is 2 / 7 = 0.2857.

Neighbor Set

In Ultipa's Jaccard Similarity algorithm, the following points have to be noted when collecting the neighbor sets of two target nodes to compute their similarity:

• There is no repeated nodes in the neighbor set;
• Self-loop is ignored;
• Any edge between the two target nodes is ignored;
• Edge direction is ignored.

In the graph above, when computing the similarity between node u and node v, the neighbor sets for the two nodes are N_u = {a,b,c,d,e} and N_v = {d,e,f}, so their Jaccard similarity is 2 / 6 = 0.3333.

In practice, you may need to convert some node properties into node schemas in order to calculate the similarity index that is based on common neighbors, just as the Jaccard Similarity. For instance, when considering the similarity between two applications, information like phone number, email, device IP, etc. of the application might have been stored as properties of @application node schema; they need to be designed as nodes and incorporated into the graph in order to be used for comparison.

Syntax

• Command: algo(similarity)
• Parameters:

This algorithm has two calculation modes:

1. Pairing: when ids/uuids and ids2/uuids2 are both configured, pairing nodes in the first group with nodes in the second group (Cartesian product) to compute pair-wise similarities.
2. Selection: when only ids/uuids is configured, for each node in the group, computing pair-wise similarities between it and all other nodes in the graph in order to select the most similar nodes, the returned top_list includes all nodes that have similarity > 0 with it and is ordered by the descending similarity.

Examples

The example graph is as follows:

File Writeback

algo(similarity).params({
  ids: "userC",
  ids2: ["userA", "userB", "userD"],
  type: "jaccard"
}).write({
  file:{ 
    filename: "sc"
  }
})

Results: File sc

userC,userA,0.25
userC,userB,0.5
userC,userD,0

algo(similarity).params({
  uuids: [1,2,3,4],
  type: "jaccard"
}).write({
  file:{ 
    filename: "list"
  }
})

Results: File list

userA,userC:0.250000;userB:0.200000;userD:0.166667;
userB,userC:0.500000;userD:0.250000;userA:0.200000;
userC,userB:0.500000;userA:0.250000;
userD,userB:0.250000;userA:0.166667;

Direct Return

algo(similarity).params({ 
  uuids: [1], 
  uuids2: [2,3,4],
  type: "jaccard"
}) as jacc
return jacc 
order by jacc.similarity desc

Results: jacc

algo(similarity).params({
  uuids: [1,2],
  type: "jaccard",
  top_limit: 1
}) as top
return top

Results: top

Stream Return

algo(similarity).params({ 
  uuids: [3], 
  uuids2: [1,2,4],
  type: "jaccard"
}).stream() as jacc
where jacc.similarity > 0
return jacc

Results: jacc

algo(similarity).params({
  uuids: [1],
  type: "jaccard",
  top_limit: 2
}).stream() as top
return top

Results: top