This paper presents a novel model for electrical circuits, called the compact port-Hamiltonian equations. The authors combine three main themes: port-Hamiltonian energy-based modeling, circuit structural analysis, and structural analysis of differential-algebraic equations (DAE). The resulting model exhibits simplicity, symmetry, and numerical properties, including that the resulting DAE always has index at most 1. The authors provide evidence through proofs and numerical results and position their work in the context of existing research on the port-Hamiltonian theory and structural amenability (S-amenability). \par The paper emphasizes the significance of the port-Hamiltonian concept in bridging mathematical theory and physics and its potential for suggesting new computational approaches. The authors highlight the power of S-amenability and demonstrate that their proposed model is both port-Hamiltonian and S-amenable. They also discuss the unexpected advantage of having index at most 1, attributing it to the adherence to the port-Hamiltonian principle that the Hamiltonian should be an algebraic function of the state variables. \par The application of port-Hamiltonian theory to electrical circuits is an active area of research, as evidenced by the references provided in the paper. While previous works explored aspects such as the selection of a ground node and transforming the Modified Nodal Analysis (MNA) equations into port-Hamiltonian form, the authors claim that their contribution of combining port-Hamiltonian and S-amenable properties, as well as their proof of the main result via Kruskal's algorithm (KA), appears to be novel. They highlight the advantages of their method, such as the ability to automate the generation of code for simulating circuits and the potential for adaptation to other programming languages. The authors acknowledge that their current system lacks the property of a ``Dirac join'', which is a crucial feature of the port-Hamiltonian theory. They express the priority of providing this property in future research, citing a previous port-Hamiltonian {\sc Modelica} system as an example.