Positive spanning sets (PSSs) are families of vectors that span a given linear
space through non-negative linear combinations. Despite certain classes of PSSs
being well understood, a complete characterization of PSSs remains elusive.
In this paper, we explore a relatively understudied relationship between positive
spanning sets and strongly edge-connected digraphs, in that the former can be viewed
as a generalization of the latter. We leverage this connection to define a
decomposition structure for positive spanning sets inspired by the ear
decomposition from digraph theory.