Metrics for Parametric Families of Networks

• URL: http://arxiv.org/abs/2509.22549v1
• Date: Fri, 26 Sep 2025 16:31:28 GMT
• Title: Metrics for Parametric Families of Networks
• Authors: Mario Gómez, Guanqun Ma, Tom Needham, Bei Wang,
• Abstract summary: Building on a Gromov-Wasserstein variant of optimal transport, we define a family of parameterized Gromov-Wasserstein distances.<n>We establish foundational properties of these distances, showing that they subsume several existing metrics in the literature.<n>We prove our distances can be consistently approximated in random graph and random metric space settings via empirical estimates from generative models.
• Score: 5.29459046551606
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: 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.

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