# Variational Bayes model averaging for graphon functions and motif frequencies inference in W-graph models

arXiv: https://arxiv.org/abs/1310.6150 · HTML: https://mlsanity.com/paper/1310.6150/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2013.

## Built on by (most cited first, 2 of 2)

- [Joint Network Topology Inference via a Shared Graphon Model](https://mlsanity.com/paper/2209.08223/) (2022)
- [Asymptotics of ℓ2 Regularized Network Embeddings](https://mlsanity.com/paper/2201.01689/) (2022)

## Abstract (arXiv)

W-graph refers to a general class of random graph models that can be seen as a random graph limit. It is characterized by both its graphon function and its motif frequencies. In this paper, relying on an existing variational Bayes algorithm for the stochastic block models along with the corresponding weights for model averaging, we derive an estimate of the graphon function as an average of stochastic block models with increasing number of blocks. In the same framework, we derive the variational posterior frequency of any motif. A simulation study and an illustration on a social network complete our work.