# On the Number of Edges of the Frechet Mean and Median Graphs

arXiv: https://arxiv.org/abs/2105.14397 · HTML: https://mlsanity.com/paper/2105.14397/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 30 references that are in the map.
- First posted on arXiv 30 May 2021.

## Builds on (most cited first, 7 of 7)

- [Metrics for Graph Comparison: A Practitioner's Guide](https://mlsanity.com/paper/1904.07414/) (2019)
- [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)
- [Network classification with applications to brain connectomics](https://mlsanity.com/paper/1701.08140/) (2017)
- [Nonparametric Bayes Modeling of Populations of Networks](https://mlsanity.com/paper/1406.7851/) (2014)
- [On clustering network-valued data](https://mlsanity.com/paper/1606.02401/) (2016)
- [Geometry of Graph Edit Distance Spaces](https://mlsanity.com/paper/1505.08071/) (2015)

## Built on by (most cited first, 1 of 1)

- [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)

The availability of large datasets composed of graphs creates an unprecedented need to invent novel tools in statistical learning for graph-valued random variables. To characterize the average of a sample of graphs, one can compute the sample Frechet mean and median graphs. In this paper, we address the following foundational question: does a mean or median graph inherit the structural properties of the graphs in the sample? An important graph property is the edge density; we establish that edge density is an hereditary property, which can be transmitted from a graph sample to its sample Frechet mean or median graphs, irrespective of the method used to estimate the mean or the median. Because of the prominence of the Frechet mean in graph-valued machine learning, this novel theoretical result has some significant practical consequences.