  This paper is an extension of the previous work of Chui, Filbir, and Mhaskar
(Appl. Comput. Harm. Anal. 38 (3) 2015:489-509), not only from numeric data to
include non-numeric data as in that paper, but also from undirected graphs to
directed graphs (called digraphs, for simplicity). Besides theoretical
development, this paper introduces effective mathematical tools in terms of
certain data-dependent orthogonal systems for function representation and
analysis directly on the digraphs. In addition, this paper also includes
algorithmic development and discussion of various experimental results on such
data-sets as CORA, Proposition, and Wiki-votes.
