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

Yasutaka Mizui,Shigeyuki Miyagi,Osamu Sakai,Tetsuya Kojima

doi:10.3390/sym9120309

Abstract

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.

Highlights

Graph theory provides for us a graphical approach to a system containing various elements with connections between them [1,2]
In comparison with the previous achievements based on numerical finite-difference methods [10,11,12,15], direct visualization of reactions based on graph theory is applied here, and we focus on graphical classification of nodes or species on statistical aspects that are missing in our previous studies [8,9]
For such systems as medium-sized chemical reaction networks, which are neither so small as several numbers of reactions nor too large with more than 1000 species, we demonstrate suitable macroscopic measures by graphical diagrams based on multi-centrality indices

Summary

Introduction

Graph theory provides for us a graphical approach to a system containing various elements with connections between them [1,2]. After definitions of a node (for one species) and an edge (for each reaction) for a display in a graph, centrality indices of nodes derived from the graph work as representatives of chemical roles in the system, such as agents, intermediates, and products Except for such microscopic points of view, approaches have not been accomplished for describing macroscopic properties of graphs for chemical reaction networks that contain several tens of species. Symmetry 2017, 9, 309 similar features to electronic information processing or mechanical systems [13,14] Another example of graphical network approaches for medium-sized chemical complexity was on numerical calculations of rate equations in plasma-enhanced chemical reactions, and the calculated results were visualized in reaction pathways in a graph to summarize complicated time evolutions of densities of species [15].

Analysis of Reaction Networks in Plasma Chemistry

Distributions

Discussion

Histograms

Conclusions