# Circular planar electrical networks, Split systems, and Phylogenetic networks

@inproceedings{Forcey2021CircularPE, title={Circular planar electrical networks, Split systems, and Phylogenetic networks}, author={S. Forcey}, year={2021} }

We study a new invariant of circular planar electrical networks, well known to phylogeneticists: the circular split system. We use our invariant to answer some open questions about levels of complexity of networks and their related Kalmanson metrics. The key to our analysis is the realization that certain matrices arising from weighted split systems are studied in another guise: the Kron reductions of Laplacian matrices of planar electrical networks. Specifically we show that a response matrix… Expand

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