Krackhardt's connectedness for a digraph \(G\) is equal to the fraction of all dyads, \(\{i,j\}\), such that there exists an undirected path from \(i\) to \(j\) in \(G\). (This, in turn, is just the density of the weak reachability graph of \(G\).) Obviously, the connectedness score ranges from 0 (for the null graph) to 1 (for weakly connected graphs).
Connectedness is one of four measures (connectedness, efficiency, hierarchy, and lubness) suggested by Krackhardt for summarizing hierarchical structures. Each corresponds to one of four axioms which are necessary and sufficient for the structure in question to be an outtree; thus, the measures will be equal to 1 for a given graph iff that graph is an outtree. Deviations from unity can be interpreted in terms of failure to satisfy one or more of the outtree conditions, information which may be useful in classifying its structural properties.