# Metrics for Parametric Families of Networks

arXiv: https://arxiv.org/abs/2509.22549 · HTML: https://mlsanity.com/paper/2509.22549/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 56 references that are in the map.
- First posted on arXiv 26 Sep 2025.

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

- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (2017)
- [Foundations and modelling of dynamic networks using Dynamic Graph Neural Networks: A survey](https://mlsanity.com/paper/2005.07496/) (2020)
- [Generalized Spectral Clustering via Gromov-Wasserstein Learning](https://mlsanity.com/paper/2006.04163/) (2020)
- [Aligning Time Series on Incomparable Spaces](https://mlsanity.com/paper/2006.12648/) (2020)
- [The Z-Gromov-Wasserstein Distance](https://mlsanity.com/paper/2408.08233/) (2024)
- [Structured Transforms Across Spaces with Cost-Regularized Optimal Transport](https://mlsanity.com/paper/2311.05788/) (2023)
- [Capturing Dynamics of Time-Varying Data via Topology](https://mlsanity.com/paper/2010.05780/) (2020)
- [Spatio-temporal Persistent Homology for Dynamic Metric Spaces](https://mlsanity.com/paper/1812.00949/) (2018)

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

- [The Observable Wasserstein Distance](https://mlsanity.com/paper/2605.09916/) (2026)

## Abstract (arXiv)

We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family of parameterized Gromov-Wasserstein distances for comparing such parametric data, including time-varying metric spaces induced by collective motion, temporally evolving weighted social networks, and random graph models. We establish foundational properties of these distances, showing that they subsume several existing metrics in the literature, and derive theoretical approximation guarantees. In particular, we develop computationally tractable lower bounds and relate them to graph statistics commonly used in random graph theory. Furthermore, we prove that our distances can be consistently approximated in random graph and random metric space settings via empirical estimates from generative models. Finally, we demonstrate the practical utility of our framework through a series of numerical experiments.