Scaling Unicyclic Graph Analysis: Automated Generation, Augmentation, and Machine Learning-Driven Prediction

Unicyclic graphs featuring a single cycle within a connected structure are crucial in modeling chemistry, biology, and information science networks. Traditional analysis methods, reliant on combinatorics, struggle with scalability for larger graphs. This paper introduces an automated framework for generating, augmenting, and analyzing unicyclic graphs using machine learning to predict key indices like degree distance. The framework enhances training datasets by systematically generating configurations and introducing structural diversity through edge perturbation and node reattachment. Evaluating models such as XGBoost and Support Vector Regression, we show that predictions closely match exact values, particularly for larger, unseen graphs. This approach improves scalability and accuracy, advancing graph analysis and network science.