I don't know any book exclusively about graph theory applied to electrical circuits, the following two touch on the subject: - Circuit Simulation by Najm - Linear System Theory by Chen. read more
My line of thinking of circuit diagrams in terms of graph theory led me to the observation that in a series-reduced tree, the idea of a series correlates to a circuit wired in series. To reiterate, a series-reduced tree has no node with exactly two edges coming out of it. read more