# Representation Learning for Scale-free Networks

arXiv: https://arxiv.org/abs/1711.10755 · HTML: https://mlsanity.com/paper/1711.10755/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2017.

## Built on by (most cited first, 4 of 4)

- [Network Representation Learning: From Preprocessing, Feature Extraction to Node Embedding](https://mlsanity.com/paper/2110.07582/) (2021)
- [CenGCN: Centralized Convolutional Networks with Vertex Imbalance for Scale-Free Graphs](https://mlsanity.com/paper/2202.07826/) (2022)
- [Zoo Guide to Network Embedding](https://mlsanity.com/paper/2305.03474/) (2023)
- [Network Alignment](https://mlsanity.com/paper/2504.11367/) (2025)

## Abstract (arXiv)

Network embedding aims to learn the low-dimensional representations of vertexes in a network, while structure and inherent properties of the network is preserved. Existing network embedding works primarily focus on preserving the microscopic structure, such as the first- and second-order proximity of vertexes, while the macroscopic scale-free property is largely ignored. Scale-free property depicts the fact that vertex degrees follow a heavy-tailed distribution (i.e., only a few vertexes have high degrees) and is a critical property of real-world networks, such as social networks. In this paper, we study the problem of learning representations for scale-free networks. We first theoretically analyze the difficulty of embedding and reconstructing a scale-free network in the Euclidean space, by converting our problem to the sphere packing problem. Then, we propose the "degree penalty" principle for designing scale-free property preserving network embedding algorithm: punishing the proximity between high-degree vertexes. We introduce two implementations of our principle by utilizing the spectral techniques and a skip-gram model respectively. Extensive experiments on six datasets show that our algorithms are able to not only reconstruct heavy-tailed distributed degree distribution, but also outperform state-of-the-art embedding models in various network mining tasks, such as vertex classification and link prediction.