The usefulness of topological indices

Abstract

A huge number of topological graph measures have been defined and investigated. It turned out that various graph measures failed to solve problems meaningfully in the context of characterizing graphs. Reasons for this range from selecting redundant and unfavorable graph invariants and the fact that many of those measures have been defined in an unreflected manner. In this paper, we extend the debate in the literature to find useful properties of structural graph measures. For this, we investigate the usefulness of topological indices for graphs quantitatively by assigning a feature vector to graph that contains ‘useful’ properties represented by certain measures. We show examples and compare the usefulness by using this apparatus based on distance measures and on a agglomerative clustering task.