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Updated: Jul 7, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

Structural information content of networks: graph entropy based on local vertex functionals.

Matthias Dehmer¹, Frank Emmert-Streib

¹Institute of Discrete Mathematics and Geometry, Vienna University of Technology, TU Vienna, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria. mdehmer@geometrie.tuwien.ac.at

Computational Biology and Chemistry

|February 5, 2008

Summary

We introduce graph entropy as a measure of structural information content in graphs. This efficient computation method is applicable to large chemical graphs, revealing their properties.

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Area of Science:

Graph theory
Chemical informatics
Information theory

Background:

Assessing structural information in graphs is crucial for various scientific domains.
Existing methods for calculating graph properties can be computationally intensive.
A need exists for efficient and scalable measures of graph complexity.

Purpose of the Study:

To define and compute the structural information content of graphs using graph entropy.
To establish a computationally efficient method for calculating graph entropy.
To demonstrate the application of graph entropy to chemical graphs.

Main Methods:

Defining graph entropy based on local vertex functionals.
Utilizing Dijkstra's algorithm to compute j-spheres for local vertex functionals.
Proving polynomial time complexity for graph entropy calculation.
Applying the method to analyze chemical graphs.

Main Results:

Graph entropy is proposed as a measure of structural information content.
The calculation of graph entropy and local vertex functionals is shown to have polynomial time complexity.
Numerical results for chemical graphs are presented, highlighting their properties.

Conclusions:

Graph entropy provides an efficient and scalable measure for the structural information content of graphs.
The polynomial time complexity enables the analysis of large and complex graph structures, particularly in chemistry.
This approach offers new insights into the properties of chemical graphs.