# Graph Classification via Deep Learning with Virtual Nodes

arXiv: https://arxiv.org/abs/1708.04357 · HTML: https://mlsanity.com/paper/1708.04357/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Aug 2017.

## Built on by (most cited first, 30 of 30)

- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [KITS: Inductive Spatio-Temporal Kriging with Increment Training Strategy](https://mlsanity.com/paper/2311.02565/) (2023)
- [VN-EGNN: E(3)-Equivariant Graph Neural Networks with Virtual Nodes Enhance Protein Binding Site Identification](https://mlsanity.com/paper/2404.07194/) (2024)
- [Probabilistic Graph Rewiring via Virtual Nodes](https://mlsanity.com/paper/2405.17311/) (2024)
- [Understanding Virtual Nodes: Oversquashing and Node Heterogeneity](https://mlsanity.com/paper/2405.13526/) (2024)
- [FlowGNN: A Dataflow Architecture for Real-Time Workload-Agnostic Graph Neural Network Inference](https://mlsanity.com/paper/2204.13103/) (2022)
- [GenGNN: A Generic FPGA Framework for Graph Neural Network Acceleration](https://mlsanity.com/paper/2201.08475/) (2022)
- [Learning Large Graph Property Prediction via Graph Segment Training](https://mlsanity.com/paper/2305.12322/) (2023)
- [Search to Capture Long-range Dependency with Stacking GNNs for Graph Classification](https://mlsanity.com/paper/2302.08671/) (2023)
- [Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning](https://mlsanity.com/paper/2506.19482/) (2025)
- [Next Level Message-Passing with Hierarchical Support Graphs](https://mlsanity.com/paper/2406.15852/) (2024)
- [Vision HgNN: An Electron-Micrograph is Worth Hypergraph of Hypernodes](https://mlsanity.com/paper/2408.11351/) (2024)
- [Short-Range Oversquashing](https://mlsanity.com/paper/2511.20406/) (2025)
- [DOTIN: Dropping Task-Irrelevant Nodes for GNNs](https://mlsanity.com/paper/2204.13429/) (2022)
- [TacoGFN: Target-conditioned GFlowNet for Structure-based Drug Design](https://mlsanity.com/paper/2310.03223/) (2023)
- [Inference of Sequential Patterns for Neural Message Passing in Temporal Graphs](https://mlsanity.com/paper/2406.16552/) (2024)
- [wav2graph: A Framework for Supervised Learning Knowledge Graph from Speech](https://mlsanity.com/paper/2408.04174/) (2024)
- [Whole-Graph Representation Learning For the Classification of Signed Networks](https://mlsanity.com/paper/2409.20073/) (2024)
- [Tired of Over-smoothing? Stress Graph Drawing Is All You Need!](https://mlsanity.com/paper/2211.10579/) (2022)
- [Sampling Foundational Transformer: A Theoretical Perspective](https://mlsanity.com/paper/2408.05822/) (2024)
- [Multi-Source Knowledge-Based Hybrid Neural Framework for Time Series Representation Learning](https://mlsanity.com/paper/2408.12409/) (2024)
- [Multi-Knowledge Fusion Network for Time Series Representation Learning](https://mlsanity.com/paper/2408.12423/) (2024)
- [Kriformer: A Novel Spatiotemporal Kriging Approach Based on Graph Transformers](https://mlsanity.com/paper/2409.14906/) (2024)
- [Hypergraph-based multi-scale spatio-temporal graph convolution network for Time-Series anomaly detection](https://mlsanity.com/paper/2410.22256/) (2024)
- [Introduction to Graph Neural Networks for Machine Learning Engineers](https://mlsanity.com/paper/2412.19419/) (2024)
- [BuildSTG: A Multi-building Energy Load Forecasting Method using Spatio-Temporal Graph Neural Network](https://mlsanity.com/paper/2507.20838/) (2025)
- [Virtual Nodes based Heterogeneous Graph Convolutional Neural Network for Efficient Long-Range Information Aggregation](https://mlsanity.com/paper/2509.23660/) (2025)
- [NAG: A Unified Native Architecture for Encoder-free Text-Graph Modeling in Language Models](https://mlsanity.com/paper/2601.22657/) (2026)
- [Pulmonary Embolism Risk Stratification from CTPA and Medical Records: Vascular Graphs Are Not All You Need](https://mlsanity.com/paper/2606.25956/) (2026)
- [Physics-Refined Spatiotemporal Forecasting on Open-Boundary Hydrologic Graphs](https://mlsanity.com/paper/2610.01765/) (2026)

## Abstract (arXiv)

Learning representation for graph classification turns a variable-size graph into a fixed-size vector (or matrix). Such a representation works nicely with algebraic manipulations. Here we introduce a simple method to augment an attributed graph with a virtual node that is bidirectionally connected to all existing nodes. The virtual node represents the latent aspects of the graph, which are not immediately available from the attributes and local connectivity structures. The expanded graph is then put through any node representation method. The representation of the virtual node is then the representation of the entire graph. In this paper, we use the recently introduced Column Network for the expanded graph, resulting in a new end-to-end graph classification model dubbed Virtual Column Network (VCN). The model is validated on two tasks: (i) predicting bio-activity of chemical compounds, and (ii) finding software vulnerability from source code. Results demonstrate that VCN is competitive against well-established rivals.