# BScNets: Block Simplicial Complex Neural Networks

arXiv: https://arxiv.org/abs/2112.06826 · HTML: https://mlsanity.com/paper/2112.06826/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 54 references that are in the map.
- First posted on arXiv 13 Dec 2021.

## Builds on (most cited first, 28 of 28)

- [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)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Predicting multicellular function through multi-layer tissue networks](https://mlsanity.com/paper/1707.04638/) (2017)
- [Simplicial Neural Networks](https://mlsanity.com/paper/2010.03633/) (2020)
- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplacian](https://mlsanity.com/paper/1807.05044/) (2018)
- [Principled Simplicial Neural Networks for Trajectory Prediction](https://mlsanity.com/paper/2102.10058/) (2021)
- [Cell Complex Neural Networks](https://mlsanity.com/paper/2010.00743/) (2020)
- [SkipGNN: Predicting Molecular Interactions with Skip-Graph Networks](https://mlsanity.com/paper/2004.14949/) (2020)
- [Link Prediction with Persistent Homology: An Interactive View](https://mlsanity.com/paper/2102.10255/) (2021)
- [Inductive Link Prediction for Nodes Having Only Attribute Information](https://mlsanity.com/paper/2007.08053/) (2020)
- [Data-Centric AI Requires Rethinking Data Notion](https://mlsanity.com/paper/2110.02491/) (2021)
- [The Effects of Evolutionary Adaptations on Spreading Processes in Complex Networks](https://mlsanity.com/paper/1810.04545/) (2018)
- [Disrupting Resilient Criminal Networks through Data Analysis: The case of Sicilian Mafia](https://mlsanity.com/paper/2003.05303/) (2020)
- [Vaccination strategies against COVID-19 and the diffusion of anti-vaccination views](https://mlsanity.com/paper/2009.13674/) (2020)

## Built on by (most cited first, 21 of 21)

- [Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks](https://mlsanity.com/paper/2304.10031/) (2023)
- [Simplicial Attention Networks](https://mlsanity.com/paper/2204.09455/) (2022)
- [Convolutional Learning on Simplicial Complexes](https://mlsanity.com/paper/2301.11163/) (2023)
- [TopoBench: A Framework for Benchmarking Topological Deep Learning](https://mlsanity.com/paper/2406.06642/) (2024)
- [Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes](https://mlsanity.com/paper/2309.12971/) (2023)
- [Facilitating Graph Neural Networks with Random Walk on Simplicial Complexes](https://mlsanity.com/paper/2310.19285/) (2023)
- [TopoGCL: Topological Graph Contrastive Learning](https://mlsanity.com/paper/2406.17251/) (2024)
- [Tensor-view Topological Graph Neural Network](https://mlsanity.com/paper/2401.12007/) (2024)
- [Topo-MLP : A Simplicial Network Without Message Passing](https://mlsanity.com/paper/2312.11862/) (2023)
- [Link Prediction without Graph Neural Networks](https://mlsanity.com/paper/2305.13656/) (2023)
- [Tensor-Fused Multi-View Graph Contrastive Learning](https://mlsanity.com/paper/2410.15247/) (2024)
- [Topology-Preserving Neural Operator Learning via Hodge Decomposition](https://mlsanity.com/paper/2605.13834/) (2026)
- [Zoo Guide to Network Embedding](https://mlsanity.com/paper/2305.03474/) (2023)
- [Continuous Simplicial Neural Networks](https://mlsanity.com/paper/2503.12919/) (2025)
- [Attribute-Enhanced Similarity Ranking for Sparse Link Prediction](https://mlsanity.com/paper/2412.00261/) (2024)
- [Cover Learning for Large-Scale Topology Representation](https://mlsanity.com/paper/2503.09767/) (2025)
- [Full-Spectrum Graph Neural Networks: Expressive and Scalable](https://mlsanity.com/paper/2605.05759/) (2026)
- [Quotient Complex Transformer (QCformer) for Perovskite Data Analysis](https://mlsanity.com/paper/2505.09174/) (2025)
- [Leveraging Personalized PageRank and Higher-Order Topological Structures for Heterophily Mitigation in Graph Neural Networks](https://mlsanity.com/paper/2507.16347/) (2025)
- [From Classical to Topological Neural Networks Under Uncertainty](https://mlsanity.com/paper/2602.10266/) (2026)
- [Weisfeiler Lehman Test on Combinatorial Complexes: Generalized Expressive Power of Topological Neural Networks](https://mlsanity.com/paper/2605.00725/) (2026)

## Abstract (arXiv)

Simplicial neural networks (SNN) have recently emerged as the newest direction in graph learning which expands the idea of convolutional architectures from node space to simplicial complexes on graphs. Instead of pre-dominantly assessing pairwise relations among nodes as in the current practice, simplicial complexes allow us to describe higher-order interactions and multi-node graph structures. By building upon connection between the convolution operation and the new block Hodge-Laplacian, we propose the first SNN for link prediction. Our new Block Simplicial Complex Neural Networks (BScNets) model generalizes the existing graph convolutional network (GCN) frameworks by systematically incorporating salient interactions among multiple higher-order graph structures of different dimensions. We discuss theoretical foundations behind BScNets and illustrate its utility for link prediction on eight real-world and synthetic datasets. Our experiments indicate that BScNets outperforms the state-of-the-art models by a significant margin while maintaining low computation costs. Finally, we show utility of BScNets as the new promising alternative for tracking spread of infectious diseases such as COVID-19 and measuring the effectiveness of the healthcare risk mitigation strategies.