= Edge deletion preserves recurrence
Deleting an <edge> of a locally finite <recurrent graph> leaves <recurrent Markov chain> connected components. On an infinite component choose a root away from the deleted <edge>'s endpoints, so its <vertex degree> does not change. The <Rayleigh monotonicity principle> increases resistance to wired outer boundaries, and <effective resistance to infinity> therefore remains infinite. Finite components are <recurrent Markov chain> too. This is a recurrence-type comparison; at an endpoint, changes in the <vertex degree> factor prevent a blanket monotonicity claim about first-return <probabilities>.
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