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On the Persistence of Higher-Order Interactions in Real-World Hypergraphs (SDM'22)

This repository contains the source code for the paper On the Persistence of Higher-Order Interactions in Real-World Hypergraphs by Hyunjin Choo and Kijung Shin, to be presented at SDM 2022.

In this work, we empirically investigate the persistence of higher-order interactions (HOIs) in 13 real-world hypergraphs from 6 domains. We define the measure of the persistence of HOIs, and using the measure, we closely examine the persistence at 3 different levels (hypergraphs, groups, and nodes), with a focus on patterns, predictability, and predictors.

  • Patterns: We reveal power-laws in the persistence and examine how they vary depending on the size of HOIs. Then, we explore relations between the persistence and 16 group- or node-level structural features, and we find some (e.g., entropy in the sizes of hyperedges including them) closely related to the persistence.
  • Predictibility: Based on the 16 structural features, we assess the predictability of the future persistence of HOIs. Additionally, we examine how the predictability varies depending on the sizes of HOIs and how long we observe HOIs.
  • Predictors: We find strong group- and node-level predictors of the persistence of HOIs, through Gini importance-based feature selection. The strongest predictors are (a) the number of hyperedges containing the HOI and (b) the average (weighted) degree of the neighbors of each node in the HOIs.

Supplementary Document

Please see supplementary.

Datasets

All datasets are available at this link.

Domain Dataset # Nodes # Hyperedges Time Range Time Unit
Coatuhorship DBLP 1,924,991 3,700,067 83 1 Year
Geology 1,256,385 1,590,335 219 1 Year
History 1,014,734 1,812,511 219 1 Year
Contact High 327 172,035 84 1 Day
Primary 242 106,879 649 6 Hours
Email Enron 143 10,883 43 1 Month
Eu 998 234,760 75 2 Weeks
NDC Classes 1,161 49,724 118 2 Years
Substances 5,311 112,405 118 2 Years
Tags math.sx 1,629 822,059 89 1 Month
ubuntu 3,029 271,233 104 1 Month
Threads math.sx 176,445 719,792 85 1 Month
ubuntu 125,602 192,947 92 1 Month

Requirements

To install requirements, run the following command on your terminal:

pip install -r requirements.txt

Measurement of the persistence of HOIs

To measure the persistence of HOIs, run these commands:

./compile.sh
./run.sh $dataset [interval|interval_front] $number_of_time_units $size_of_hois $maximum_size_of_he [0:others|1:coauthorship] $number_of_observed_time_units $number_of_observed_time_units_for_features

We provide the running example codes for measureing the persistence of HOIs, by running this command.

./run_batch.sh

Preprocessing

To preprocess before analyzing the persistence of HOIs, run these commands:

./count_time_units.sh
./graph.sh

Global Analysis: Persistence vs. Frequency

To obtain the global patterns in the persistence of HOIs, run these commands:

python3 main.py -f $dataset -d global_analysis -m $number_of_time_units -i $number_of_observed_time_units
python3 main.py -d global_stat

We provide the running example codes for global analysis, by running this command.

./global_analysis.sh

Local Analysis: Features vs. Persistence

To assess the local patterns in the persistence of HOIs, run these commands:

python3 main.py -f $dataset -d [local_analysis|local_group_group|local_node_group|local_node_node] -m $number_of_time_units -i $number_of_observed_time_units -t $number_of_observed_time_units_for_features
python3 main.py -d local_stat

We provide the running example codes for local analysis, by running this command.

./local_analysis.sh

Predictability and Predictors

To examine the predictability of the persistence of HOIs, run these commands:

python3 main.py -f $dataset -d [pred_1|pred_1_past|pred_2|pred_2_past] -m $number_of_time_units -i $number_of_observed_time_units -t $number_of_observed_time_units_for_features
python3 main.py -d pred_feature_selection -i $number_of_observed_time_units -t $number_of_observed_time_units_for_features
python3 main.py -d predictability -i $number_of_observed_time_units

We provide the running example codes for local analysis, by running this command.

./pred.sh

Reference

This code is free and open source for only academic/research purposes (non-commercial). If you use this code as part of any published research, please acknowledge the following paper.