# Node Classification via Simplicial Interaction with Augmented Maximal Clique Selection

arXiv: https://arxiv.org/abs/2509.23568 · HTML: https://mlsanity.com/paper/2509.23568/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 50 references that are in the map.
- First posted on arXiv 28 Sep 2025.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [What are higher-order networks?](https://mlsanity.com/paper/2104.11329/) (2021)
- [PageRank beyond the Web](https://mlsanity.com/paper/1407.5107/) (2014)
- [A Review of Stochastic Block Models and Extensions for Graph Clustering](https://mlsanity.com/paper/1903.00114/) (2019)
- [Community Detection in Hypergraphs, Spiked Tensor Models, and Sum-of-Squares](https://mlsanity.com/paper/1705.02973/) (2017)
- [Motif Graph Neural Network](https://mlsanity.com/paper/2112.14900/) (2021)
- [Higher-order Graph Convolutional Networks](https://mlsanity.com/paper/1809.07697/) (2018)
- [Customized Subgraph Selection and Encoding for Drug-drug Interaction Prediction](https://mlsanity.com/paper/2411.01535/) (2024)
- [Node classification in networks via simplicial interactions](https://mlsanity.com/paper/2310.10114/) (2023)

## Abstract (arXiv)

Considering higher-order interactions allows for a more comprehensive understanding of network structures beyond simple pairwise connections. While leveraging all cliques in a network to handle higher-order interactions is intuitive, it often leads to computational inefficiencies due to overlapping information between higher-order and lower-order cliques. To address this issue, we propose an augmented maximal clique strategy. Although using only maximal cliques can reduce unnecessary overlap and provide a concise representation of the network, certain nodes may still appear in multiple maximal cliques, resulting in imbalanced training data. Therefore, our augmented maximal clique approach selectively includes some non-maximal cliques to mitigate the overrepresentation of specific nodes and promote more balanced learning across the network. Comparative analyses on synthetic networks and real-world citation datasets demonstrate that our method outperforms approaches based on pairwise interactions, all cliques, or only maximal cliques. Finally, by integrating this strategy into GNN-based semi-supervised learning, we establish a link between maximal clique-based methods and GNNs, showing that incorporating higher-order structures improves predictive accuracy. As a result, the augmented maximal clique strategy offers a computationally efficient and effective solution for higher-order network learning.