# How to compute the barycenter of a weighted graph

arXiv: https://arxiv.org/abs/1605.04148 · HTML: https://mlsanity.com/paper/1605.04148/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 May 2016.

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

- [A Sobering Look at Tabular Data Generation via Probabilistic Circuits](https://mlsanity.com/paper/2603.23016/) (2026)
- [Stochastic Langevin Monte Carlo for (weakly) log-concave posterior distributions](https://mlsanity.com/paper/2301.03077/) (2023)

## Abstract (arXiv)

Discrete structures like graphs make it possible to naturally and flexibly model complex phenomena. Since graphs that represent various types of information are increasingly available today, their analysis has become a popular subject of research. The graphs studied in the field of data science at this time generally have a large number of nodes that are not fairly weighted and connected to each other, translating a structural specification of the data. Yet, even an algorithm for locating the average position in graphs is lacking although this knowledge would be of primary interest for statistical or representation problems. In this work, we develop a stochastic algorithm for finding the Frechet mean of weighted undirected metric graphs. This method relies on a noisy simulated annealing algorithm dealt with using homogenization. We then illustrate our algorithm with two examples (subgraphs of a social network and of a collaboration and citation network).