It is shown that a network can be constructed on a given set of host computers such that the possibility of a network partition resulting from network node and link failure can be ruled out with an arbitrarily high degree of confidence. More precisely, a class of networks is exhibited on any given number of host nodes so that the probability of a network partition decreases exponentially with only a linear increase in connectivity cost. It has long been a folk theorem in network theory that as one increases the budget for the number of links of a network, the reliability of the network can be increased by a judicious choice of network topology. This paper makes this intuitive statement precise and analyzes one class of networks to illustrate it: bipartite networks where host nodes are connected to each of a set of hub nodes. The result has significant implications for availability of distributed databases and feasibility of the three-phase commit protocol which guarantees crash recovery in distributed transactions.