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Related Experiment Video

Updated: Feb 5, 2026

Traditional Trail Making Test Modified into Brand-new Assessment Tools: Digital and Walking Trail Making Test

Published on: November 23, 2019

Closed trail distance in a biconnected graph.

Vaclav Snasel¹, Pavla Drazdilova¹, Jan Platos¹

¹Department of Computer Science, Faculty of Electrical Engineering and Computer Science, VŠB - Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava, Czech Republic.

|September 1, 2018

Summary

This study introduces a new graph metric to measure node distance, considering higher connectivity in complex networks like fullerene graphs. The metric captures cyclical interdependencies, offering a novel approach to graph analysis.

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Area of Science:

Graph theory
Network analysis
Computational chemistry

Background:

Graphs are fundamental to representing complex systems like social networks and chemical structures.
Existing distance metrics in graphs do not fully capture higher-order connectivity.
K-connectivity is a crucial property in many real-world networks.

Purpose of the Study:

To propose a novel graph metric for calculating node distances.
To account for increased connectivity, particularly in k-connected subgraphs.
To reflect cyclical interdependencies within graph components.

Main Methods:

Development of a new distance metric for graphs.
Derivation of a new component model for graph analysis.
Application and illustration of the metric on various graph types, including fullerene graphs.

Main Results:

A novel metric accurately reflects cyclical interdependencies in highly connected graphs.
The proposed component model provides new insights into graph structures.
Demonstrated applicability across diverse graph examples.

Conclusions:

The new metric enhances graph analysis by incorporating higher connectivity.
This approach is valuable for understanding complex systems with cyclical relationships.
The findings contribute to the field of network science and graph theory.