# Geometry of Graph Edit Distance Spaces

arXiv: https://arxiv.org/abs/1505.08071 · HTML: https://mlsanity.com/paper/1505.08071/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2015.

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

- [On the Number of Edges of the Frechet Mean and Median Graphs](https://mlsanity.com/paper/2105.14397/) (2021)

## Abstract (arXiv)

In this paper we study the geometry of graph spaces endowed with a special class of graph edit distances. The focus is on geometrical results useful for statistical pattern recognition. The main result is the Graph Representation Theorem. It states that a graph is a point in some geometrical space, called orbit space. Orbit spaces are well investigated and easier to explore than the original graph space. We derive a number of geometrical results from the orbit space representation, translate them to the graph space, and indicate their significance and usefulness in statistical pattern recognition.