Detection of brain network abnormalities by graph invariants in Alzheimer's disease using MRI images.

Alzheimer's disease is a major cause of dementia in older adults. It involves gradual changes in brain function that result in cognitive decline, affecting memory, reasoning, and executive skills. The accurate detection of structural abnormalities in brain networks is crucial for early diagnosis and disease staging. This study presents a graph-based framework that analyzes abnormalities in brain networks of Alzheimer's patients using six distance-based topological indices: Szeged index, Graovac-Ghorbani index, Padmakar-Ivan index, Mostar index, Wiener index, and Normalized Graovac-Ghorbani index. These indices effectively characterize the structural properties of brain networks and identify disruptions linked to disease progression. The proposed framework first constructs brain graphs from MRI images using the Brightness Distance Matrix method, which captures the spatial relationships between pixels. Then, the constructed brain graphs are modeled using the Watts and Strogatz small-world model to normalize the topological indices. The normalized indices serve as input features for various machine learning models, including decision trees, logistic regression, support vector machines, and a multi-layer neural network. Among these models, a refined neural network model achieves the highest classification accuracy of 89.45%, confirming the value of topological indices as interpretable biomarkers for disease staging. This framework demonstrates the potential of graph-theoretic approaches for detecting Alzheimer's-related brain network alterations and offers a scalable, interpretable, and privacy-friendly solution.