# Approximate Fr'echet Mean for Data Sets of Sparse Graphs

arXiv: https://arxiv.org/abs/2105.04062 · HTML: https://mlsanity.com/paper/2105.04062/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 35 references that are in the map.
- First posted on arXiv 10 May 2021.

## Builds on (most cited first, 9 of 9)

- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [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)
- [Network histograms and universality of blockmodel approximation](https://mlsanity.com/paper/1312.5306/) (2013)
- [Hypothesis Testing For Network Data in Functional Neuroimaging](https://mlsanity.com/paper/1407.5525/) (2014)
- [Modeling Network Populations via Graph Distances](https://mlsanity.com/paper/1904.07367/) (2019)
- [The eigenvalues of stochastic blockmodel graphs](https://mlsanity.com/paper/1803.11551/) (2018)
- [Spectral Graph Forge: Graph Generation Targeting Modularity](https://mlsanity.com/paper/1801.01715/) (2018)
- [Spectral Representations of Graphons in Very Large Network Systems Control](https://mlsanity.com/paper/1911.01536/) (2019)

## Abstract (arXiv)

To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Fr'echet mean. In this work, we equip a set of graph with the pseudometric defined by the ℓ2 norm between the eigenvalues of their respective adjacency matrix . Unlike the edit distance, this pseudometric reveals structural changes at multiple scales, and is well adapted to studying various statistical problems on sets of graphs. We describe an algorithm to compute an approximation to the Fr'echet mean of a set of undirected unweighted graphs with a fixed size.