  The two- and all-terminal reliabilities of the Brecht-Colbourn ladder and the
generalized fan have been calculated exactly for arbitrary size as well as
arbitrary individual edge and node reliabilities, using transfer matrices of
dimension four at most. While the all-terminal reliabilities of these graphs
are identical, the special case of identical edge ($p$) and node ($\rho$)
reliabilities shows that their two-terminal reliabilities are quite distinct,
as demonstrated by their generating functions and the locations of the zeros of
the reliability polynomials, which undergo structural transitions at $\rho =
\displaystyle {1/2}$.
