# Comparison of old and new algorithms to compute the $$s,t$$-network reliability
Suppose $$G$$ is a graph (= network) with two specified nodes $$s$$ (the source) and $$t$$ (the terminal). Further the edges of $$G$$ are assumed to be operational with fixed (and independent) probability $$p$$. Then the $$s,t$$- network reliability is defined as the probability $$nr(G)$$ (which is a polynomial in $$p$$) of an operational path connecting $$s$$ and $$t$$. Calculating $$nr(G)$$ is known to to be #P-complete. In this thesis we present some old techniques which have existed since the 1950’s, as well as four new algorithms for calculating $$nr(G)$$. Because these algorithms are all coded in Mathematica as a common platform, they can be compared in a fair way.