Mahya Ghandehari, an associate professor in the University of Delaware’s Department of Mathematical Sciences, was recently awarded the NSF Combinatorics program grant titled “A graphon-based approach to seriation and an application in GSP.” The primary objective of this research is to develop a systematic mathematical framework for analyzing and visualizing large networks. We live in an era defined by data, much of which is organized as large and intricate networks—ranging from social and biological systems to neural cell networks. These real-world networks are often highly complex, and understanding their structure is essential for designing robust and efficient algorithms to process them. By integrating two distinct areas of mathematics—Discrete Mathematics and Analysis—Ghandehari aims to extract large-scale features of networks using mathematical limit theories of discrete structures.

A fundamental challenge in network analysis is uncovering the hidden spatial layout of a network, that is, labeling its vertices according to their spatial features. This is known as the seriation problem, a well-known and challenging issue in machine learning. In recent years, various heuristics and algorithms have been developed for approximate versions of the seriation problem, but there is limited theoretical understanding of why these methods are effective or how they might be extended to multi-dimensional cases. Supported by this grant, Ghandehari investigates important questions regarding the robustness and consistency of spectral seriation and its generalizations to higher dimensions. Potential practical applications of this research include data analysis in fields such as sociology, psychology, and image processing. In particular, Ghandehari explores how spatial graphons can provide instance-independent methods for graph signal processing in real-world networks. As part of this grant, Ghandehari will supervise PhD student research on related problems and plans to organize two events at the University of Delaware: one for high school students and another for undergraduate students