A graph-theoretic condition for irreducibility of a set of cone   preserving matrices
  Given a closed, convex and pointed cone K in R^n, we present a result which infers K-irreducibility of sets of K-quasipositive matrices from strong connectedness of certain bipartite digraphs. The matrix-sets are defined via products, and the main result is relevant to applications in biology and chemistry. Several examples are presented. 
Murad Banaji and Andrew Burbanks
math.CO