We present a natural proof of a recent and surprising result of Gregory Berkolaiko interpreting the Courant nodal defect as a Morse index. This proof is inspired by a nice paper of Miroslav Fiedler published in 1975.
"Magnetic interpretation of the nodal defect on graphs." Anal. PDE 6 (5) 1235 - 1242, 2013. https://doi.org/10.2140/apde.2013.6.1235