weakly chained diagonally dominant matrices and basic definitions

Question

I would like some direction on where to look for more information about directed graphs of a square matrix and the connection to weakly chained diagonally dominant matrices. I want very basic definitions that for some reason I cannot find in wikipedia searches on M-matrices and obviously diagonal dominance, weak diagonal dominance, and weakly chained diagonal dominance, which is a small piece of my attempt to address boundary conditions of a reaction diffusion problem. Any help would be appreciated - textbook references that give explicit definitions or simple examples would be preferential. Thank you all