Dassios, Ioannis K.Ioannis K.DassiosKeane, AndrewAndrewKeaneCuffe, PaulPaulCuffe2019-05-212019-05-212019 the A2019-01-20Mathematics2227-7390http://hdl.handle.net/10197/10576Calculating nodal voltages and branch current flows in a meshed network is fundamental to electrical engineering. This work demonstrates how such calculations can be performed using the eigenvalues and eigenvectors of the Laplacian matrix which describes the connectivity of the electrical network. These insights should permit the functioning of electrical networks to be understood in the context of spectral analysis.enThis is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).Laplacian matrixPower flowAdmittance matrixVoltage profileJournal Article7110.3390/math70101062019-05-13SFI/15/SPP/E3125SFI/15/IA/3074https://creativecommons.org/licenses/by-nc-nd/3.0/ie/