# Influential Simplices Mining via Simplicial Convolutional Network

arXiv: https://arxiv.org/abs/2307.05841 · HTML: https://mlsanity.com/paper/2307.05841/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 64 references that are in the map.
- First posted on arXiv 11 Jul 2023.

## Builds on (most cited first, 21 of 21)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [Principled Simplicial Neural Networks for Trajectory Prediction](https://mlsanity.com/paper/2102.10058/) (2021)
- [The physics of higher-order interactions in complex systems](https://mlsanity.com/paper/2110.06023/) (2021)
- [Epidemic processes in complex networks](https://mlsanity.com/paper/1408.2701/) (2014)
- [Vital nodes identification in complex networks](https://mlsanity.com/paper/1607.01134/) (2016)
- [Generalized Network Dismantling](https://mlsanity.com/paper/1801.01357/) (2018)
- [Network dismantling](https://mlsanity.com/paper/1603.08883/) (2016)
- [Scalable Graph Neural Network-based framework for identifying critical nodes and links in Complex Networks](https://mlsanity.com/paper/2012.15725/) (2020)
- [Identifying vital nodes through augmented random walks on higher-order networks](https://mlsanity.com/paper/2305.06898/) (2023)
- [Analysing Scientific Collaborations of New Zealand Institutions using Scopus Bibliometric Data](https://mlsanity.com/paper/1709.02897/) (2017)
- [Unraveling the effects of multiscale network entanglement on disintegration of empirical systems](https://mlsanity.com/paper/2008.05368/) (2020)

## Built on by (most cited first, 2 of 2)

- [HOG-Diff: Higher-Order Guided Diffusion for Graph Generation](https://mlsanity.com/paper/2502.04308/) (2025)
- [Cooperative Network Learning for Large-Scale and Decentralized Graphs](https://mlsanity.com/paper/2311.02117/) (2023)

## Abstract (arXiv)

Simplicial complexes have recently been in the limelight of higher-order network analysis, where a minority of simplices play crucial roles in structures and functions due to network heterogeneity. We find a significant inconsistency between identifying influential nodes and simplices. Therefore, it remains elusive how to characterize simplices' influence and identify influential simplices, despite the relative maturity of research on influential nodes (0-simplices) identification. Meanwhile, graph neural networks (GNNs) are potent tools that can exploit network topology and node features simultaneously, but they struggle to tackle higher-order tasks. In this paper, we propose a higher-order graph learning model, named influential simplices mining neural network (ISMnet), to identify vital h-simplices in simplicial complexes. It can tackle higher-order tasks by leveraging novel higher-order presentations: hierarchical bipartite graphs and higher-order hierarchical (HoH) Laplacians, where targeted simplices are grouped into a hub set and can interact with other simplices. Furthermore, ISMnet employs learnable graph convolutional operators in each HoH Laplacian domain to capture interactions among simplices, and it can identify influential simplices of arbitrary order by changing the hub set. Empirical results demonstrate that ISMnet significantly outperforms existing methods in ranking 0-simplices (nodes) and 2-simplices. In general, this novel framework excels in identifying influential simplices and promises to serve as a potent tool in higher-order network analysis.