The document discusses the challenges and solutions related to distributed k-betweenness centrality computation in complex networks using technologies like Spark and GraphX. It highlights the difficulties of betweenness computation on large graphs, especially regarding node information access and graph size limitations. Key results indicate that while the implementation performs well on large diameter graphs, it struggles with small diameter graphs and requires careful tuning.

1. Distributed K-
Betweenness
Complex Network Analysis
Daniel Marcous and Yotam Sandbank
dmarcous@gmail.com
yotamsandbank@gmail.com

2. Centrality
❖ Core concept in complex network analysis
❖ Different measures:
❖ Closeness
❖ Degree
❖ Betweenness

3. Betweenness
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4. Betweenness computation
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5. Betweenness computation

6. Betweenness computation

7. Betweenness computation

8. Distributed Betweenness
❖ Independent computation for each node
❖ Why not run on different machines?
❖ Betweenness computation not implemented in GraphX

9. Distributed Betweenness
❖ Algorithm:
❖ Divide nodes between machines
❖ For each machine, compute the Betweenness contribution of each node to every
other node in the graph
❖ Aggregate results from all machines
❖ Problems:
❖ Can’t get information about a specific node in GraphX
❖ Need to copy graph to every machine (goes bad with big graphs)

10. Distributed Betweenness
❖ Solutions:
❖ Can’t get information about a specific node in GraphX
❖ GraphX Pregel API
❖ Run 1 iteration, with every node passing its identity to all its neighbors
❖ Need to copy graph to every machine (goes wrong with big graphs)
❖ We didn’t find a good solution for this problem
❖ How can we avoid copying the whole graph to every machine?

11. Distributed K-Betweenness
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Quotes by Adriana Iamnitchi , University of South Florida

12. Distributed K-Betweenness
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13. Distributed K-Betweenness
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14. Implementation
❖ Technology :
❖ Spark 1.5.2
❖ Scala 2.10
❖ GraphX 1.5.2 (+ Pregel API)
❖ Steps :
❖ Create K-graphlets
❖ Pregel
❖ Parallel BC calculation - contribution of vertex X to other vertices BC
❖ Local for each vertex’ graphlet
❖ Brandes
❖ Also parallelized for each vertex in k-graphlet
❖ BC Aggregation - final kBC score for each vertex
❖ Reduce

15. Code

16. Code

17. Usage

18. Tuning

19. Do it yourself
❖ The project can be found in github:
❖ https://github.com/dmarcous/spark-betweenness
❖ Accessible as a Spark Package !
❖ http://spark-packages.org/package/dmarcous/spark-betweenness
❖ spark code (scala / java), spark-shell, spark-submit, pySpark APIs

20. Experiment design
❖ Amazon EMR cluster
❖ 1 master
❖ 4 worker nodes
❖ r3.2xlarge
❖ 8 vcpu
❖ 61 GB RAM
❖ 160 GB SSD
❖ 6 Datasets
❖ Different sizes (|E| / |V|)
❖ Different diameters
❖ Implementations
❖ spark-betweenness
❖ networkX

21. Results
Spark Single Description Type Name
240 31 3 9 5156 3015 Small random generated Random HW2
601 210 3 8 88234 4039 Social circles Social Facebook
-1 349 4
2160 -1 3 16 428156 58228 Friendship network Social Birghtkite
489 -1 3 44 925872 334863 Customer co-purchases Social Amazon
5707 -1 4
-1 -1 5
139 -1 3 849 2766607 1965206 Road net of California Infrastructure roadNet-Ca
356 -1 4
638 -1 5
85 -1 3 1054 3843324 1379917 Road net of Texas Infrastructure roadNet-TX
305 -1 4
600 -1 5
-1 means it either crashed or didn’t finish in a long time (over an hour)

22. Results

23. Results
❖ Performs great on graphs with large diameter
❖ Large K-graphlets are “impossible” to store in memory and send between machines
❖ Not good for graphs with small diameter (very slow, sometimes crashes)
❖ Very hard to tune (how many cores, memory for each process, and so on..)

24. Conclusions
❖ Distributed Betweenness – good idea in theory, hard to implement
❖ Multi-threaded on a single strong machine might do the job
❖ Our implementation – great for large diameter graphs (road networks,
power grids, and more)