With the aid of Menger's theorem,Hassler Whitney was able to present a characterization of k-connected graphs. Theorem 5.17 A nontrivial graph G is k-connected for some integer k >2 if and only if for each pair u,v of distinct vertices of G there are at least k internally disjoint u-v paths in G. We have introduced two measures of good connection:invulnerability to deletions and multiplicity of alternative paths.Extending Whitney's Theorem, we show that these two notions are the same,for both vertex deletions and edge deletions,and for both graphs and digraphs