A Unified Approach to Compute Kirchhoff Index and Resistance Distances of Molecular Networks

The study of complex networks relies significantly on the notions of resistance distances [Formula: see text] and the Kirchhoff index (Kf) to get insights into network connection and strength. This research explores the Kirchhoff index and spectra of complicated networks. The Kirchhoff index is examined comparatively to identify and explain its significant values in the contexts of pharmaceutical and electrical networks. The novelty of our research is in the application of this approach to chemical networks. However, it has been investigated on different networks. These networks illustrate the molecular networks of inhibitors and boronic acid both used in the pharmaceutical field for medical treatment and in advanced drug discovery. We primarily use topological indices to compute the eigenvalues of the networks. The eigenvalues of the Laplacian matrix are computed for the selected networks which provides the spectral characteristics. Laplacian matrix characterizes the energy levels and vibrational patterns of the molecular structure. This assists researchers in identifying possible drug candidates with better stability characteristics We provide a novel approach for molecular networks that enables increasing and lowering the resistance of selected edges by using the resistors. The computational methods are efficient making them appropriate for large-scale networks in both fields. They also have a short execution time.