ENTROPY APPROACH THROUGH GRAPH-THEORY FOR STUDYING THE DEGREE OF ORDER IN ONE-DIMENSIONAL DISTRIBUTIONS OF OBJECTS

Graph theory, through the minimal spanning tree (MST), and information theory, through the concept of entropy, are used to define a new para meter gamma which quantitatively characterizes the degree of order (or disorder) in 1D sets of points. Theoretical calculations and results obtained from various computer-simulated distributions of points are c ompared. For well-chosen conditions which are specified, a good agreem ent is noted. Finally, a method which is particularly easy to implemen t is proposed to evaluate the parameter gamma for any real or simulate d 1D distribution of points.