Measuring the complexity of directed graphs: A polynomial-based approach


Autoři: Matthias Dehmer aff001;  Zengqiang Chen aff002;  Frank Emmert-Streib aff004;  Shailesh Tripathi aff001;  Abbe Mowshowitz aff006;  Alexei Levitchi aff001;  Lihua Feng aff007;  Yongtang Shi aff008;  Jin Tao aff009
Působiště autorů: Institute for Intelligent Production, Faculty for Management, University of Applied Sciences Upper Austria, Steyr, Austria aff001;  College of Artificial Intelligence, Nankai University, Tianjin, China aff002;  Department of Biomedical Computer Science and Mechatronics, UMIT - The Health and Lifesciences University, A-6060 Hall in Tyrol, Austria aff003;  Predictive Medicine and Data Analytics Lab, Department of Signal Processing, Tampere University, Tampere, Finland aff004;  Institute of Biosciences and Medical Technology, Tampere, Finland aff005;  Department of Computer Science, The City College of New York (CUNY), 138th Street at Convent Avenue, New York, United States of America aff006;  School of Mathematics and Statistics, Central South University, Changsha, China aff007;  Center for Combinatorics and LPMC, Nankai University, Tianjin, China aff008;  Department of Electrical Engineering and Automation, Aalto University, Espoo, Finland aff009;  College of Engineering, Peking University, Beijing, China aff010
Vyšlo v časopise: PLoS ONE 14(11)
Kategorie: Research Article
doi: 10.1371/journal.pone.0223745

Souhrn

In this paper, we define novel graph measures for directed networks. The measures are based on graph polynomials utilizing the out- and in-degrees of directed graphs. Based on these polynomial, we define another polynomial and use their positive zeros as graph measures. The measures have meaningful properties that we investigate based on analytical and numerical results. As the computational complexity to compute the measures is polynomial, our approach is efficient and can be applied to large networks. We emphasize that our approach clearly complements the literature in this field as, to the best of our knowledge, existing complexity measures for directed graphs have never been applied on a large scale.

Klíčová slova:

Directed graphs – Distance measurement – Eigenvalues – Entropy – Game theory – Polynomials – Random graphs – Real numbers


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Článek vyšel v časopise

PLOS One


2019 Číslo 11