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Graphical Classification in Multi-Centrality-Index Diagrams for Complex Chemical Networks

Electronic Systems Engineering, The University of Shiga Prefecture, 2500 Hassakacho, Hikone, Shiga 522-8533, Japan
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Symmetry 2017, 9(12), 309; https://doi.org/10.3390/sym9120309
Received: 22 October 2017 / Revised: 5 December 2017 / Accepted: 5 December 2017 / Published: 9 December 2017
(This article belongs to the Special Issue Graph Theory)
Various sizes of chemical reaction network exist, from small graphs of linear networks with several inorganic species to huge complex networks composed of protein reactions or metabolic systems. Huge complex networks of organic substrates have been well studied using statistical properties such as degree distributions. However, when the size is relatively small, statistical data suffers from significant errors coming from irregular effects by species, and a macroscopic analysis is frequently unsuccessful. In this study, we demonstrate a graphical classification method for chemical networks that contain tens of species. Betweenness and closeness centrality indices of a graph can create a two-dimensional diagram with information of node distribution for a complex chemical network. This diagram successfully reveals systematic sharing of roles among species as a semi-statistical property in chemical reactions, and distinguishes it from the ones in random networks, which has no functional node distributions. This analytical approach is applicable for rapid and approximate understanding of complex chemical network systems such as plasma-enhanced reactions as well as visualization and classification of other graphs. View Full-Text
Keywords: chemical reaction network; centrality index; statistical analysis; random graph chemical reaction network; centrality index; statistical analysis; random graph
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Mizui, Y.; Kojima, T.; Miyagi, S.; Sakai, O. Graphical Classification in Multi-Centrality-Index Diagrams for Complex Chemical Networks. Symmetry 2017, 9, 309.

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