The construction of most reliable networks is investigated. In particular, the study of restricted edge connectivity shows that general Harary graphs are max-minmi for all i=, +1,...,2-3. As a consequence, this implies that for each pair of positive integers n and e, there is a graph of n vertices and e edges that is max-minmi for all i=,+1,...,2-3. General Harary graphs that are max-minmi for all i=,+1,...,2-2 are also constructed. 2003 Published by Elsevier B.V.
