NoAH

This is the official implementation of NoAH (Node Attribute based Hypergraph generator), which is described in the following paper:

• Attributed Hypergraph Generation with Realistic Interplay Between Structure and Attributes
  Jaewan Chun*, Seokbum Yoon*, Minyoung Choe, Geon Lee, Kijung Shin
  ICDM 2025

The paper is accessible in the following link:

• http://arxiv.org/abs/2509.21838

Overview

In many real-world scenarios, interactions happen in a group-wise manner with multiple entities, and therefore, hypergraphs are a suitable tool to accurately represent such interactions. Hyperedges in real-world hypergraphs are not composed of randomly selected nodes but are instead formed through structured processes. Consequently, various hypergraph generative models have been proposed to explore fundamental mechanisms underlying hyperedge formation. However, most existing hypergraph generative models do not account for node attributes, which can play a significant role in hyperedge formation. As a result, these models fail to reflect the interactions between structure and node attributes.
To address the issue above, we propose NOAH, a stochastic hypergraph generative model for attributed hypergraphs. NOAH utilizes the core–fringe node hierarchy to model hyperedge formation as a series of node attachments and determines attachment probabilities based on node attributes. We further introduce NOAHFIT, a parameter learning procedure that allows NOAH to replicate a given real-world hypergraph. Through experiments on nine datasets across four different domains, we show that NOAH with NOAHFIT more accurately reproduces the structure–attribute interplay observed in the real-world hypergraphs than eight baseline hypergraph generative models, in terms of six metrics.

Datasets

We provide the code for NoAH. We provide the information on the datasets used in the experiment below.

Dataset	Cores	Fringes	Nodes	Hyperedges	Attribute Dimension
Citeseer	597	861	1,458	1,079	3,703
Cora	841	1,547	2,388	1,072	1,433
High School	288	39	327	7,818	12
Workspace	71	21	92	788	5
Amazon Music	379	727	1,106	686	7
Yelp Resaurant	273	292	565	594	9
Yelp Bar	625	609	1,234	1,188	15
Devops	2,003	3,007	5,010	5,684	429
Patents	894	3,564	4,458	4,669	2,170

Requirements

NoAH and the evaluation codes were run with the following Python packages:

Package	Version
networkx	3.1
numpy	1.26.4
scikit-learn	1.3.2
scipy	1.10.1
snap-stanford	6.0.0
torch	2.3.0
tqdm	4.65.0

You can install them via pip:

pip install -r requirements.txt

How to Run NoAH

1. Run NoAH/run_NoAH.sh, with designated configuration. In particular, you can adjust (1) dataset, (2) seed (random seed), (3) epoch, (4) lr (learning rate), (5) device (CUDA device), (6) wdegreeset (set of degree penalty weight), and (7) wsizeset (set of cardinality penalty weight).
2. Run metric/run_metric.sh.