# Emergence of Soft Communities from Geometric Preferential Attachment

arXiv: https://arxiv.org/abs/1501.06835 · HTML: https://mlsanity.com/paper/1501.06835/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2015.

## Built on by (most cited first, 8 of 8)

- [A Multi-purposed Unsupervised Framework for Comparing Embeddings of Undirected and Directed Graphs](https://mlsanity.com/paper/2112.00075/) (2021)
- [Evaluating Node Embeddings of Complex Networks](https://mlsanity.com/paper/2102.08275/) (2021)
- [Zoo Guide to Network Embedding](https://mlsanity.com/paper/2305.03474/) (2023)
- [Symmetry-driven embedding of networks in hyperbolic space](https://mlsanity.com/paper/2406.10711/) (2024)
- [Beyond MMD: Evaluating Graph Generative Models with Geometric Deep Learning](https://mlsanity.com/paper/2512.14241/) (2025)
- [Hyperbolic Benchmarking Unveils Network Topology-Feature Relationship in GNN Performance](https://mlsanity.com/paper/2406.02772/) (2024)
- [Uncovering the hidden core-periphery structure in hyperbolic networks](https://mlsanity.com/paper/2406.19953/) (2024)
- [Bayesian Latent Space Models for Graphs Are Misspecified: Toward Robust Inference via Generalized Posteriors](https://mlsanity.com/paper/2605.18927/) (2026)

## Abstract (arXiv)

All real networks are different, but many have some structural properties in common. There seems to be no consensus on what the most common properties are, but scale-free degree distributions, strong clustering, and community structure are frequently mentioned without question. Surprisingly, there exists no simple generative mechanism explaining all the three properties at once in growing networks. Here we show how latent network geometry coupled with preferential attachment of nodes to this geometry fills this gap. We call this mechanism geometric preferential attachment (GPA), and validate it against the Internet. GPA gives rise to soft communities that provide a different perspective on the community structure in networks. The connections between GPA and cosmological models, including inflation, are also discussed.