# A common variable minimax theorem for graphs

arXiv: https://arxiv.org/abs/2107.14747 · HTML: https://mlsanity.com/paper/2107.14747/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 16 references that are in the map.
- First posted on arXiv 30 Jul 2021.

## Builds on (most cited first, 2 of 2)

- [Clustering on Multi-Layer Graphs via Subspace Analysis on Grassmann Manifolds](https://mlsanity.com/paper/1303.2221/) (2013)
- [Spectral Discovery of Jointly Smooth Features for Multimodal Data](https://mlsanity.com/paper/2004.04386/) (2020)

## Built on by (most cited first, 5 of 5)

- [Robust Inference of Manifold Density and Geometry by Doubly Stochastic Scaling](https://mlsanity.com/paper/2209.08004/) (2022)
- [Spatiotemporal Analysis Using Riemannian Composition of Diffusion Operators](https://mlsanity.com/paper/2201.08530/) (2022)
- [On Learning what to Learn: heterogeneous observations of dynamics and establishing (possibly causal) relations among them](https://mlsanity.com/paper/2406.06812/) (2024)
- [Conformal Disentanglement and Latent-Space Curation: A Neural Framework for Perspective Synthesis, Differentiation and Targeted Generation](https://mlsanity.com/paper/2408.15344/) (2024)
- [Complex Interpolation of Matrices with an application to Multi-Manifold Learning](https://mlsanity.com/paper/2604.14118/) (2026)

## Abstract (arXiv)

Let G = G1 = (V, E1), dots, Gm = (V, Em) be a collection of m graphs defined on a common set of vertices V but with different edge sets E1, dots, Em. Informally, a function f :V rightarrow ℝ is smooth with respect to Gk = (V,Ek) if f(u) ~ f(v) whenever (u, v) ∈ Ek. We study the problem of understanding whether there exists a nonconstant function that is smooth with respect to all graphs in G, simultaneously, and how to find it if it exists.