Temporal Hypergraph Motifs

Source code for the paper Temporal Hypergraph Motifs, Geon Lee and Kijung Shin, Knowledge and Information Systems (2023). This is an extension of THyMe+: Temporal Hypergraph Motifs and Fast Algorithms for Exact Counting, Geon Lee and Kijung Shin, ICDM 2021.

Group interactions arise in our daily lives (email communications, on-demand ride sharing, comment interactions on online communities, to name a few), and they together form hypergraphs that evolve over time. Given such temporal hypergraphs, how can we describe their underlying design principles? If their sizes and time spans are considerably different, how can we compare their structural and temporal characteristics? In this work, we define 96 temporal hypergraph motifs (TH-motifs), and propose the relative occurrences of their instances as an answer to the above questions. TH-motifs categorize the relational and temporal dynamics among three connected hyperedges that appear within a short time. For scalable analysis, we develop THyMe+, a fast and exact algorithm for counting the instances of TH-motifs in massive hypergraphs, and show that THyMe+ is at most 2,163X faster while requiring less space than baseline. In addition to exact counting algorithms, we design three versions of sampling algorithms for approximate counting. We theoretically analyze the accuracy of the proposed methods, and we empirically show that the most advanced algorith, THyMe-A* is up to 11.1X more accurate than baseline approaches. Using the algorithms, we investigate 11 real-world temporal hypergraphs from various domains. We demonstrate that TH-motifs provide important information useful for downstream tasks and reveal interesting patterns, including the striking similarity between temporal hypergraphs from the same domain.

Datasets

• The original datasets are available here.
• The processed datasets (email-Enron & contact-primary) are available in here.

How to Run Exact Counting Algorithms

• To run demos, execute following commend in code:

./run_(dp/thyme/thymeP).sh

• To run DP, THyMe, and THyMe+ with specified dataset and time interval (delta), execute following commends in code:

g++ -O3 -std=c++11 main_(dp/thyme/thymeP).cpp -o run;
./run (dataset) (delta)

• Results will be saved in results as:

Filename: (dataset)_(delta)_(dp/thyme/thymeP).txt

Runtime (sec.)
1   (# of instances of TH-motif 1)
2   (# of instances of TH-motif 2)
...
96  (# of instances of TH-motif 96)

How to Run Approximate Counting Algorithms

• To run demos, execute following commend in code:

./run_(approx/approx+/approx++).sh

• To run THyMe-A, THyMe-A+, and THyMe-A* with specified dataset, time interval (delta), sampling time interval ratio (T), and the number of samples (S), execute following commends in code:

g++ -O3 -std=c++11 main_(approx/approx+/approx++).cpp -o run;
./run (dataset) (delta) (T) (S)

• The sampling time interval is set to $T\cdot(T_{max}-T_{min})$ where $T_{min}$ and $T_{max}$ are the minimum and maximum timestamp of the entire dataset.
• Results will be saved in results as:

Filename: (dataset)_(delta)_(S)_(T)_(approx/approx+/approx++).txt

Runtime (sec.)
1   (estimated # of instances of TH-motif 1)
2   (estimated # of instances of TH-motif 2)
...
96  (estimated # of instances of TH-motif 96)

Contact Information

If you have any questions, please contact Geon Lee.