Hypergraph Motifs: Concepts, Algorithms, and Discoveries

Source code for the paper Hypergraph Motifs: Concepts, Algorithms, and Discoveries, Geon Lee, Jihoon Ko, Kijung Shin, VLDB 2020.

We propose Hypergraph Motifs (h-motifs), whose occurrences capture local structural patterns of real-world hypergraphs.

H-motifs describe connectivity patterns of three connected hyperedges with the following properties:

• Exhaustive: h-motifs capture connectivity patterns of all possible three connected hyperedges
• Unique: connectivity pattern of any three connected hyperedges is captured by exactly one h-motif
• Size Independent: h-motifs capture connectivity patterns independently of the sizes of hyperedges

MoCHy (Motif Counting in Hypergraphs) is a family of parallel algorithms for counting hypergraph motifs' instances.

• MoCHy-E (MoCHy Exact) exactly counts the instances of each h-motif.
• MoCHy-A (MoCHy Approximate): approximately counts the instances of each h-motif.
• The advanced approximated version MoCHy-A+ is up to 25X more accurate than MoCHy-A, and it is up to 32X faster than MoCHy-E.

Datasets

• The sample dataset is available here.
• The real-world datasets used in the paper are available here or here.
• In the paper, we used datasets with unique hyperedges, where duplicated hyperedges are removed.

Input & Output Format

• The input format should be lines of hyperedges, where each line represents the nodes contained in each hyperedge.
• The index of the nodes should start from 0.
• For example, with 3 hyperedges: {0, 1, 2}, {2, 3}, and {1, 3, 4, 5}, the input file should be:

0,1,2
2,3
1,3,4,5

• The output of the code will be:

motif 1: 123
motif 2: 22
...
motif 26: 31

Running Demo

You can run demo with the sample dataset (dblp_graph.txt).

1. To run MoCHy-E, type 'run_exact.sh'.
2. To run parallelized MoCHy-E, type 'run_exact_par.sh'.
3. To run MoCHy-A, type 'run_approx_ver1.sh'.
4. To run MoCHy-A+, type 'run_approx_ver2.sh'.
5. To run parallelized MoCHy-A+, type 'run_approx_ver2_par.sh'.
6. To run memory-bounded MoCHy-A+, type 'run_approx_ver2_memory.sh'.

Terms and Conditions

If you use this code as part of any published research, please acknowledge our VLDB 2020 paper.

@article{lee2020hypergraph,
  title={Hypergraph Motifs: Concepts, Algorithms, and Discoveries},
  author={Lee, Geon and Ko, Jihoon and Shin, Kijung},
  journal={Proceedings of the VLDB Endowment},
  year={2020},
  publisher={VLDB Endowment}
}

Contact Information

If you have any questions, please contact Geon Lee ([email protected]).