Optimizing network insights: AI-Driven approaches to circulant graph based on Laplacian spectra

Abstract

Exploring the applications of Laplacian and signless Laplacian spectra extends beyond theoretical chemistry, computer science, electrical networks, and complex networks. These spectra, with their relevance, provide valuable insights into the structures of real-world networks and facilitate the prediction of their structural properties. The focal point of the study lies in the spectrum-based analysis of circulant graphs. From these analyses, crucial network measures such as mean-first passage time, average path length, spanning trees, and spectral radius are derived. This research enriches our comprehension of the interplay between graph spectra and network characteristics, offering a holistic understanding of complex networks. Consequently, it contributes to the ability to make predictions and conduct analyses across diverse scientific disciplines.