The Graphon Fourier Transform

TL;DR

This paper introduces the Graphon Fourier Transform (WFT), a new method for analyzing signals on graphons, which are limit objects of graphs, enabling transferability and efficiency in network analysis.

Contribution

The paper defines graphon signals and the WFT, demonstrating convergence of the GFT to the WFT, facilitating transferable analysis across similar graphs.

Findings

GFT converges to WFT in numerical experiments

WFT enables transferability of graph signal analysis

Centralized analysis on graphons is feasible

Abstract

In many network problems, graphs may change by the addition of nodes, or the same problem may need to be solved in multiple similar graphs. This generates inefficiency, as analyses and systems that are not transferable have to be redesigned. To address this, we consider graphons, which are both limit objects of convergent graph sequences and random graph models. We define graphon signals and introduce the Graphon Fourier Transform (WFT), to which the Graph Fourier Transform (GFT) is shown to converge. This result is demonstrated in two numerical experiments where, as expected, the GFT converges, hinting to the possibility of centralizing analysis and design on graphons to leverage transferability.