# Probability density estimation for sets of large graphs with respect to spectral information using stochastic block models

arXiv: https://arxiv.org/abs/2207.02168 · HTML: https://mlsanity.com/paper/2207.02168/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 43 references that are in the map.
- First posted on arXiv 5 Jul 2022.

## Builds on (most cited first, 11 of 11)

- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [A Systematic Survey on Deep Generative Models for Graph Generation](https://mlsanity.com/paper/2007.06686/) (2020)
- [Fr'echet Regression for Random Objects with Euclidean Predictors](https://mlsanity.com/paper/1608.03012/) (2016)
- [Metrics for Graph Comparison: A Practitioner's Guide](https://mlsanity.com/paper/1904.07414/) (2019)
- [Perfect Clustering for Stochastic Blockmodel Graphs via Adjacency Spectral Embedding](https://mlsanity.com/paper/1310.0532/) (2013)
- [Modeling Network Populations via Graph Distances](https://mlsanity.com/paper/1904.07367/) (2019)
- [A spectral method for community detection in moderately-sparse degree-corrected stochastic block models](https://mlsanity.com/paper/1506.08621/) (2015)
- [The eigenvalues of stochastic blockmodel graphs](https://mlsanity.com/paper/1803.11551/) (2018)
- [Regularized Stochastic Block Model for robust community detection in complex networks](https://mlsanity.com/paper/1903.11751/) (2019)
- [Clustering of heterogeneous populations of networks](https://mlsanity.com/paper/2107.07489/) (2021)
- [Theoretical analysis and computation of the sample Frechet mean for sets of large graphs based on spectral information](https://mlsanity.com/paper/2201.05923/) (2022)

## Abstract (arXiv)

For graph-valued data sampled iid from a distribution μ, the sample moments are computed with respect to a choice of metric. In this work, we equip the set of graphs with the pseudo-metric defined by the ℓ2 norm between the eigenvalues of the respective adjacency matrices. We use this pseudo metric and the respective sample moments of a graph valued data set to infer the parameters of a distribution hatμ and interpret this distribution as an approximation of μ. We verify experimentally that complex distributions μ can be approximated well taking this approach.