The closure of the set of roots of strongly connected reliability polynomials is the entire complex plane

The strongly connected reliability scRel ( D , p ) of a digraph D is the probability that the spanning subgraph of D consisting of the operational arcs is strongly connected, given that the vertices always operate, but each arc is independently operational with probability p ∈ [ 0 , 1 ] . We show that the closure of the set of roots of strongly connected reliability polynomials is the whole complex plane.