# Hop-Count Based Self-Supervised Anomaly Detection on Attributed Networks

arXiv: https://arxiv.org/abs/2104.07917 · HTML: https://mlsanity.com/paper/2104.07917/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 58 references that are in the map.
- First posted on arXiv 16 Apr 2021.

## Builds on (most cited first, 27 of 27)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)
- [Unsupervised Visual Representation Learning by Context Prediction](https://mlsanity.com/paper/1505.05192/) (2015)
- [Self-supervised Visual Feature Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/1902.06162/) (2019)
- [Using Self-Supervised Learning Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1906.12340/) (2019)
- [Unsupervised Learning of Video Representations using LSTMs](https://mlsanity.com/paper/1502.04681/) (2015)
- [Unsupervised Representation Learning by Sorting Sequences](https://mlsanity.com/paper/1708.01246/) (2017)
- [A Survey on Network Embedding](https://mlsanity.com/paper/1711.08752/) (2017)
- [When Does Self-Supervision Help Graph Convolutional Networks?](https://mlsanity.com/paper/2006.09136/) (2020)
- [Self-supervised Learning on Graphs: Deep Insights and New Direction](https://mlsanity.com/paper/2006.10141/) (2020)
- [Learning to See by Moving](https://mlsanity.com/paper/1505.01596/) (2015)
- [Boosting Self-Supervised Learning via Knowledge Transfer](https://mlsanity.com/paper/1805.00385/) (2018)
- [Iterative Reorganization with Weak Spatial Constraints: Solving Arbitrary Jigsaw Puzzles for Unsupervised Representation Learning](https://mlsanity.com/paper/1812.00329/) (2018)
- [Self-Supervised Graph Representation Learning via Global Context Prediction](https://mlsanity.com/paper/2003.01604/) (2020)
- [Cross and Learn: Cross-Modal Self-Supervision](https://mlsanity.com/paper/1811.03879/) (2018)
- [Scalable Anomaly Ranking of Attributed Neighborhoods](https://mlsanity.com/paper/1601.06711/) (2016)
- [Outlier Aware Network Embedding for Attributed Networks](https://mlsanity.com/paper/1811.07609/) (2018)
- [ResGCN: Attention-based Deep Residual Modeling for Anomaly Detection on Attributed Networks](https://mlsanity.com/paper/2009.14738/) (2020)
- [Unsupervised learning from video to detect foreground objects in single images](https://mlsanity.com/paper/1703.10901/) (2017)
- [Multi-scale Anomaly Detection on Attributed Networks](https://mlsanity.com/paper/1912.04144/) (2019)
- [Unsupervised Learning of Edges](https://mlsanity.com/paper/1511.04166/) (2015)
- [Semi-supervised Embedding in Attributed Networks with Outliers](https://mlsanity.com/paper/1703.08100/) (2017)
- [Outlier Detection for Text Data : An Extended Version](https://mlsanity.com/paper/1701.01325/) (2017)
- [Link Prediction with Mutual Attention for Text-Attributed Networks](https://mlsanity.com/paper/1902.11054/) (2019)

## Built on by (most cited first, 30 of 31)

- [Graph Contrastive Learning Automated](https://mlsanity.com/paper/2106.07594/) (2021)
- [Self-supervised Learning on Graphs: Contrastive, Generative,or Predictive](https://mlsanity.com/paper/2105.07342/) (2021)
- [Graph Anomaly Detection via Multi-Scale Contrastive Learning Networks with Augmented View](https://mlsanity.com/paper/2212.00535/) (2022)
- [ARC: A Generalist Graph Anomaly Detector with In-Context Learning](https://mlsanity.com/paper/2405.16771/) (2024)
- [GAD-NR: Graph Anomaly Detection via Neighborhood Reconstruction](https://mlsanity.com/paper/2306.01951/) (2023)
- [Truncated Affinity Maximization: One-class Homophily Modeling for Graph Anomaly Detection](https://mlsanity.com/paper/2306.00006/) (2023)
- [Deep Graph Anomaly Detection: A Survey and New Perspectives](https://mlsanity.com/paper/2409.09957/) (2024)
- [Bringing Your Own View: Graph Contrastive Learning without Prefabricated Data Augmentations](https://mlsanity.com/paper/2201.01702/) (2022)
- [Zero-shot Generalist Graph Anomaly Detection with Unified Neighborhood Prompts](https://mlsanity.com/paper/2410.14886/) (2024)
- [PREM: A Simple Yet Effective Approach for Node-Level Graph Anomaly Detection](https://mlsanity.com/paper/2310.11676/) (2023)
- [Self-Supervised Anomaly Detection in Computer Vision and Beyond: A Survey and Outlook](https://mlsanity.com/paper/2205.05173/) (2022)
- [Graph Anomaly Detection with Graph Neural Networks: Current Status and Challenges](https://mlsanity.com/paper/2209.14930/) (2022)
- [Generative Semi-supervised Graph Anomaly Detection](https://mlsanity.com/paper/2402.11887/) (2024)
- [A Survey of Imbalanced Learning on Graphs: Problems, Techniques, and Future Directions](https://mlsanity.com/paper/2308.13821/) (2023)
- [FreeGAD: A Training-Free yet Effective Approach for Graph Anomaly Detection](https://mlsanity.com/paper/2508.10594/) (2025)
- [Towards Digital Twin Oriented Modelling of Complex Networked Systems and Their Dynamics: A Comprehensive Survey](https://mlsanity.com/paper/2202.09363/) (2022)
- [ARISE: Graph Anomaly Detection on Attributed Networks via Substructure Awareness](https://mlsanity.com/paper/2211.15255/) (2022)
- [Cluster Aware Graph Anomaly Detection](https://mlsanity.com/paper/2409.09770/) (2024)
- [From Few-Shot to Zero-Shot: Towards Generalist Graph Anomaly Detection](https://mlsanity.com/paper/2602.18793/) (2026)
- [Normality Learning-based Graph Anomaly Detection via Multi-Scale Contrastive Learning](https://mlsanity.com/paper/2309.06034/) (2023)
- [GCTAM: Global and Contextual Truncated Affinity Combined Maximization Model For Unsupervised Graph Anomaly Detection](https://mlsanity.com/paper/2603.01806/) (2026)
- [Cross-Domain Graph Anomaly Detection via Test-Time Training with Homophily-Guided Self-Supervision](https://mlsanity.com/paper/2502.14293/) (2025)
- [OWLEYE: Zero-Shot Learner for Cross-Domain Graph Data Anomaly Detection](https://mlsanity.com/paper/2601.19102/) (2026)
- [Decoupling anomaly discrimination and representation learning: self-supervised learning for anomaly detection on attributed graph](https://mlsanity.com/paper/2304.05176/) (2023)
- [Label-based Graph Augmentation with Metapath for Graph Anomaly Detection](https://mlsanity.com/paper/2308.10918/) (2023)
- [Rethinking Contrastive Learning in Graph Anomaly Detection: A Clean-View Perspective](https://mlsanity.com/paper/2505.18002/) (2025)
- [Generalist Graph Anomaly Detection via Prototype-Based Distillation](https://mlsanity.com/paper/2605.26857/) (2026)
- [Evolutionary Router Feature Generation for Zero-Shot Graph Anomaly Detection with Mixture-of-Experts](https://mlsanity.com/paper/2602.11622/) (2026)
- [TA-GGAD: Testing-time Adaptive Graph Model for Generalist Graph Anomaly Detection](https://mlsanity.com/paper/2603.09349/) (2026)
- [NeighborDiv: Training-free Zero-shot Generalist Graph Anomaly Detection via Neighbor Diversity](https://mlsanity.com/paper/2605.20879/) (2026)

## Abstract (arXiv)

Recent years have witnessed an upsurge of interest in the problem of anomaly detection on attributed networks due to its importance in both research and practice. Although various approaches have been proposed to solve this problem, two major limitations exist: (1) unsupervised approaches usually work much less efficiently due to the lack of supervisory signal, and (2) existing anomaly detection methods only use local contextual information to detect anomalous nodes, e.g., one- or two-hop information, but ignore the global contextual information. Since anomalous nodes differ from normal nodes in structures and attributes, it is intuitive that the distance between anomalous nodes and their neighbors should be larger than that between normal nodes and their neighbors if we remove the edges connecting anomalous and normal nodes. Thus, hop counts based on both global and local contextual information can be served as the indicators of anomaly. Motivated by this intuition, we propose a hop-count based model (HCM) to detect anomalies by modeling both local and global contextual information. To make better use of hop counts for anomaly identification, we propose to use hop counts prediction as a self-supervised task. We design two anomaly scores based on the hop counts prediction via HCM model to identify anomalies. Besides, we employ Bayesian learning to train HCM model for capturing uncertainty in learned parameters and avoiding overfitting. Extensive experiments on real-world attributed networks demonstrate that our proposed model is effective in anomaly detection.