A second look at Krackhardt's graph theoretical dimensions of informal organizations

Krackhardt (1994) proposed four dimensions to describe and measure the amount of hierarchy in networks of informal organizations. We examine these conditions, suggest some relaxations and prove that they are both necessary and sufficient to guarantee an arborescence (or out-tree). In addition we suggest situations some of which are outside of informal organizations in which fewer of the conditions can be used to capture the hierarchical tree structure.

► We prove Krackhardt's graph dimensions imply an arborescence.
► We look at the modelling implications of the dimensions.
► We suggest relaxations.
► We give examples of situations in which the relaxations are appropriate.