Chapter 3. A Simple Integrated Approach to Network Complexity and Node Centrality
- PD Dr. habil. Matthias Dehmer2,3,
- Prof. Dr. Frank Emmert-Streib4
Published Online: 21 AUG 2009
DOI: 10.1002/9783527627981.ch3
Copyright © 2009 Wiley-VCH Verlag GmbH & Co. KGaA
Book Title
Analysis of Complex Networks: From Biology to Linguistics
Additional Information
How to Cite
Bonchev, D. (2009) A Simple Integrated Approach to Network Complexity and Node Centrality, in Analysis of Complex Networks: From Biology to Linguistics (eds M. Dehmer and F. Emmert-Streib), Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527627981.ch3
Editor Information
- 2
Vienna University of Technology, Discrete Mathematics and Geometry, Wiedner Hauptstraße 8–10, 1040 Vienna, Austria
- 3
University of Coimbra, Center for Mathematics, Apartado 3008, 3001-454 Coimbra, Portugal
- 4
Computational Biology and Machine Learning, Center for Cancer Research and Cell Biology, School of Medicine, Dentistry and Biomedical Sciences, Queen's University Belfast, 97 Lisburn Road, Belfast, BT9 7BL, UK
Publication History
- Published Online: 21 AUG 2009
- Published Print: 22 APR 2009
ISBN Information
Print ISBN: 9783527323456
Online ISBN: 9783527627981
- Summary
- Chapter
- References
Keywords:
- network complexity;
- node centrality;
- small-world connectivity descriptors;
- integrated centrality measure
Summary
A-series of three descriptors of network complexity is introduced by combining the vertex degree distribution with that of vertex distance. The new small-world connectivity descriptors (termed also Bourgas indices, B1–B3) mirror the increase in network complexity with increasing vertex degrees and/or with decreasing network radius (the “small-world” network signature). The individual terms of the combined distributions, defined as ratios of vertex degree and vertex distance, are in turn a-measure of vertex centrality, termed “integrated centrality.” The information theoretic descriptor-B3 emerges as sensitive complexity measure producing ordering of graphs of the same size from the minimum complexity of linear graphs (paths) through branched and cyclic graphs to complete graphs.