Autism Spectrum Disorder (ASD) is a prevalent neurological disorder. However, the multi-faceted symptoms and large individual differences among ASD patients are hindering the diagnosis process, which largely relies on subject descriptions and lacks quantitative biomarkers. To remediate such problems, this paper explores the use of graph theory and topological data analysis (TDA) to study brain activity in ASD patients and normal controls. We employ the Mapper algorithm in TDA and the distance correlation graphical model (DCGM) in graph theory to create brain state networks, then innovatively adopt complex network metrics in Graph signal processing (GSP) and physical quantities to analyze brain activities over time. Our findings reveal statistical differences in network characteristics between ASD and control groups. Compared to normal subjects, brain state networks of ASD patients tend to have decreased modularity, higher von Neumann entropy, increased Betti-0 numbers, and decreased Betti-1 numbers. These findings attest to the biological traits of ASD, suggesting less organized and more variable brain dynamics. These findings offer potential biomarkers for ASD diagnosis and deepen our understanding of its neural correlations.

Accepted by the Brain Informatics 2024 Conference. This is the final version of the paper for the conference. First author: Yuzhe Chen. Second author: Dayu Qin. Third & Corresponding author: Ercan Engin Kuruoglu