A directed graph representation based on a statistical hypothesis testing and application to citation and association structures

A statistical hypothesis testing method is developed for generating a directed graph from a matrix of nonsymmetric interactions among elements of a system. Two threshold parameters are applied to an interaction matrix in order to generate edges of the graph. Chi-square goodness-of-fit test is considered. The generated graph is plotted on a plane as a figure with hierarchically order vertices. Two applications are considered: one is the structure of literature in computer applications and cybernetics based on citation relationships; the other is the structure of scientific notions of students based on an association test in educational psychology.