[jira] [Created] (FLINK-2310) Add an Adamic-Adar Similarity example

["Andra Lungu (JIRA)" <ji...@apache.org>]

Andra Lungu created FLINK-2310:
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             Summary: Add an Adamic-Adar Similarity example
                 Key: FLINK-2310
                 URL: https://issues.apache.org/jira/browse/FLINK-2310
             Project: Flink
          Issue Type: Task
          Components: Gelly
            Reporter: Andra Lungu
            Priority: Minor


Just as Jaccard, the Adamic-Adar algorithm measures the similarity between a set of nodes. However, instead of counting the common neighbors and dividing them by the total number of neighbors, the similarity is weighted according to the vertex degrees. In particular, it's equal to log(1/numberOfEdges).

The Adamic-Adar algorithm can be broken into three steps: 
1). For each vertex, compute the log of its inverse degrees (with the formula above) and set it as the vertex value. 
2). Each vertex will then send this new computed value along with a list of neighbors to the targets of its out-edges
3). Weigh the edges with the Adamic-Adar index: Sum over n from CN of log(1/k_n)(CN is the set of all common neighbors of two vertices x, y. k_n is the degree of node n). See [2]

Prerequisites: 
- Full understanding of the Jaccard Similarity Measure algorithm
- Reading the associated literature: 
[1] http://social.cs.uiuc.edu/class/cs591kgk/friendsadamic.pdf
[2] http://stackoverflow.com/questions/22565620/fast-algorithm-to-compute-adamic-adar




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