In this section we survey the results known about the compactness of graphs, that is the smallest integer k that provides a shortest path k-IRS. We start with some general results. Recall that the compactness of G is denoted by , ( and ) denotes the linear compactness ( strict and strict-linear compactness). See Paragraph 2.5.
For convenience, for every class of graphs ,
we denote by
the value defined by: