# A family of graph GOSPA metrics for graphs with different sizes

arXiv: https://arxiv.org/abs/2506.17316 · HTML: https://mlsanity.com/paper/2506.17316/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 39 references that are in the map.
- First posted on arXiv 18 Jun 2025.

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

- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Gromov-Wasserstein Learning for Graph Matching and Node Embedding](https://mlsanity.com/paper/1901.06003/) (2019)
- [GOT: An Optimal Transport framework for Graph comparison](https://mlsanity.com/paper/1906.02085/) (2019)
- [Generalized optimal sub-pattern assignment metric](https://mlsanity.com/paper/1601.05585/) (2016)
- [A metric on the space of finite sets of trajectories for evaluation of multi-target tracking algorithms](https://mlsanity.com/paper/1605.01177/) (2016)
- [A metric for sets of trajectories that is practical and mathematically consistent](https://mlsanity.com/paper/1601.03094/) (2016)
- [Graph GOSPA metric: a metric to measure the discrepancy between graphs of different sizes](https://mlsanity.com/paper/2311.07596/) (2023)

## Abstract (arXiv)

This paper proposes a family of graph metrics for measuring distances between graphs of different sizes. The proposed metric family defines a general form of the graph generalised optimal sub-pattern assignment (GOSPA) metric and is also proved to satisfy the metric properties. Similarly to the graph GOSPA metric, the proposed graph GOSPA metric family also penalises the node attribute costs for assigned nodes between the two graphs, and the number of unassigned nodes. However, the proposed family of metrics provides more general penalties for edge mismatches than the graph GOSPA metric. This paper also shows that the graph GOSPA metric family can be approximately computed using linear programming. Simulation experiments are performed to illustrate the characteristics of the proposed graph GOSPA metric family with different choices of hyperparameters. The benefits of the proposed graph GOSPA metric family for classification tasks are also shown on real-world datasets.