puzzlef / rak-communities

Single-threaded CPU-based Raghavan Albert Kumara (RAK) algorithm, aka Label propagation Algorithm (LPA), for community detection.

Single-threaded CPU-based Raghavan Albert Kumara (RAK) algorithm for community detection.

This is an implementation of a popular label-propagation based community detection algorithm called Raghavan Albert Kumara (RAK). Here, every node is initialized with a unique label and at every step each node adopts the label that most of its neighbors currently have. In this iterative process densely connected groups of nodes form a consensus on a unique label to form communities.

When there exist multiple communities with max weight, we randomly pick one of them (non-strict approach), or pick only the first of them (strict approach). The algorithm converges when n% of vertices dont change their community membership (tolerance).

In this experiment we adjust tolerance from 0.1 to 0.0001.

Non-strict approach generally achieves better modularity, with certain exceptions (coAuthors*, road networks). I think this has to do with graph structure. See for example on coAuthorsDBLP graph.

It seems to me a tolerance of 0.05 would be a good choice.

All outputs are saved in a gist and a small part of the output is listed here. Some charts are also included below, generated from sheets. The input data used for this experiment is available from the SuiteSparse Matrix Collection. This experiment was done with guidance from Prof. Kishore Kothapalli and Prof. Dip Sankar Banerjee.

$ g++ -std=c++17 -O3 main.cxx
$ ./a.out ~/data/web-Stanford.mtx
$ ./a.out ~/data/web-BerkStan.mtx
$ ...

# Loading graph /home/subhajit/data/web-Stanford.mtx ...
# order: 281903 size: 2312497 [directed] {}
# order: 281903 size: 3985272 [directed] {} (symmetricize)
# [-0.000497 modularity] noop
# [00157.008 ms; 0003 iters.; 0.872759998 modularity] rakSeqStatic       {tolerance=1e-01}
# [00157.307 ms; 0003 iters.; 0.847129285 modularity] rakSeqStaticStrict {tolerance=1e-01}
# [00156.578 ms; 0003 iters.; 0.872759998 modularity] rakSeqStatic       {tolerance=5e-02}
# [00152.985 ms; 0003 iters.; 0.847129285 modularity] rakSeqStaticStrict {tolerance=5e-02}
# [00246.655 ms; 0005 iters.; 0.876379907 modularity] rakSeqStatic       {tolerance=1e-02}
# [00246.319 ms; 0005 iters.; 0.853610516 modularity] rakSeqStaticStrict {tolerance=1e-02}
# [00290.881 ms; 0006 iters.; 0.877100408 modularity] rakSeqStatic       {tolerance=5e-03}
# [00286.677 ms; 0006 iters.; 0.854387999 modularity] rakSeqStaticStrict {tolerance=5e-03}
# [00384.414 ms; 0008 iters.; 0.877606571 modularity] rakSeqStatic       {tolerance=1e-03}
# [00420.077 ms; 0009 iters.; 0.855403066 modularity] rakSeqStaticStrict {tolerance=1e-03}
# [00469.554 ms; 0010 iters.; 0.877725899 modularity] rakSeqStatic       {tolerance=5e-04}
# [00602.378 ms; 0013 iters.; 0.856024683 modularity] rakSeqStaticStrict {tolerance=5e-04}
# [00648.129 ms; 0014 iters.; 0.877830148 modularity] rakSeqStatic       {tolerance=1e-04}
# [00776.319 ms; 0017 iters.; 0.856140256 modularity] rakSeqStaticStrict {tolerance=1e-04}
#
# ...

References

• Near linear time algorithm to detect community structures in large-scale networks; Usha Nandini Raghavan et al. (2007)
• The University of Florida Sparse Matrix Collection; Timothy A. Davis et al. (2011)
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