The concept of Hückel molecular orbital theory is used to compute the graph energy numerically as well asnd graphically, on the base of the status of a vertex. Our aim is to explore the graph energy of various graph families on the base of the status adjacency matirx matrix and its Laplacian version. We opt for the technique of finding eigenvalues of adjacency and Laplacian matrices constructed on the base of the status of vertices. We explore the exact status sum and Laplacian status sum energies of a complete graph, complete bipartite graph, star graphs, bistar graphs, barbell graphs and graphs of two thorny rings. We also compared the obtained results of energy numerically and graphically. In this article, we extended the study of graph spectrum and energy by introducing the new concept of the status sum adjacency matrix and the Laplacian status sum adjacency matrix of a graph. We investigated and visualized these newly defined spectrums and energies of well-known graphs, such as complete graphs, complete bi-graphs, star graphs, friendship graphs, bistar graphs, barbell graphs, and thorny graphs with 3 and 4 cycles.