The usefulness of topological indices

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. (c) 2022 Published by Elsevier Inc.

Automated summary

This paper investigates the usefulness of topological graph measures and finds that many measures fail to solve problems effectively due to the selection of redundant and unfavorable graph invariants, as well as the lack of reflection in defining these measures. The paper extends the debate in the literature and quantitatively studies the usefulness of topological indices by assigning a feature vector to graphs that contains 'useful' properties represented by certain measures. The paper demonstrates examples and compares the usefulness using distance measures and an agglomerative clustering task.