# Network Representation Using Graph Root Distributions

arXiv: https://arxiv.org/abs/1802.09684 · HTML: https://mlsanity.com/paper/1802.09684/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2018.

## Built on by (most cited first, 12 of 12)

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- [Spectral embedding for dynamic networks with stability guarantees](https://mlsanity.com/paper/2106.01282/) (2021)
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- [Frameless Graph Knowledge Distillation](https://mlsanity.com/paper/2307.06631/) (2023)
- [Implications of sparsity and high triangle density for graph representation learning](https://mlsanity.com/paper/2210.15277/) (2022)
- [Asymptotics of ℓ2 Regularized Network Embeddings](https://mlsanity.com/paper/2201.01689/) (2022)
- [Community Detection Guarantees Using Embeddings Learned by Node2Vec](https://mlsanity.com/paper/2310.17712/) (2023)
- [Entrywise error bounds for low-rank approximations of kernel matrices](https://mlsanity.com/paper/2405.14494/) (2024)
- [Bias-Corrected Joint Spectral Embedding for Multilayer Networks with Invariant Subspace: Entrywise Eigenvector Perturbation and Inference](https://mlsanity.com/paper/2406.07849/) (2024)
- [Adjacency Spectral Embeddings of Correlation Networks](https://mlsanity.com/paper/2602.21055/) (2026)
- [Uncovering Locally Low-dimensional Structure in Networks by Locally Optimal Spectral Embedding](https://mlsanity.com/paper/2603.11965/) (2026)

## Abstract (arXiv)

Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. In this work we develop an alternative parameterization for a large class of exchangeable random graphs, where the nodes are independent random vectors in a linear space equipped with an indefinite inner product, and the edge probability between two nodes equals the inner product of the corresponding node vectors. Therefore, the distribution of exchangeable random graphs in this subclass can be represented by a node sampling distribution on this linear space, which we call the graph root distribution. We study existence and identifiability of such representations, the topological relationship between the graph root distribution and the exchangeable random graph sampling distribution, and estimation of graph root distributions.