Graph theory and its potential in the automatic detection of left bundle branch block

Accurate differentiation between Left Bundle Branch Block (LBBB) and its strict subtype (sLBBB) is essential for optimizing patient selection for Cardiac Resynchronization Therapy (CRT), yet remains clinically challenging. This study proposes and compares two graph-theory-based pipelines for automated classification of 12-lead electrocardiograms (ECGs) into Healthy, LBBB, and sLBBB categories. Functional connectivity graphs were constructed from inter-lead measures, including Pearson correlation, cross-correlation, and phase difference. The first approach combines Graph Signal Processing (GSP) with machine learning. Graph filtering was performed via spectral decomposition of the Laplacian matrix, selecting dominant eigenmodes and reconstructing signals through the inverse Graph Fourier Transform—integrating spatial and temporal features. The second approach converted connectivity matrices into grayscale images, classified using a Convolutional Neural Network (CNN), and incorporated Explainable AI (XAI) via Grad-CAM to visualize inter-lead interactions and enhance model transparency. The GSP-based method using phase difference and a Support Vector Machine achieved the highest performance (mean balanced accuracy = 0.8317 ), while the CNN-based approach with cross-correlation images reached 0.7646 , offering improved interpretability. Both methods distinguished pathological from healthy cases, but precise classification between LBBB and sLBBB remains challenging. These results highlight the complementary value of graph-based ECG analysis and support future hybrid models for CRT stratification.