Distance in Digraphs

The (directed) distance d⃗(u, v) from a vertex u to a vertex v in a strong digraph D is the length of a shortest u-v path in D. Although this is the standard distance in digraphs, it is not a metric. Two other distances in digraphs are introduced, each of which is a metric. The maximum distance md(u, v) between two vertices u and v in a strong digraph is defined as md(u, v) = max{d⃗(u, v), d⃗(v, u)}. The sum distance sd(u, v) is defined as sd(u, v) = d⃗(u, v) + d⃗(v, u). Several results and problems concerning these metrics and such parameters as centers, medians, and peripheries are described.