Evaluation of Transmission Properties of Networks Described with Reference Graphs Using Unevenness Coefficients

• Published in: Electronics (Basel) Vol. 10; no. 14; p. 1684
• Main Authors: Bujnowski, Sławomir, Marciniak, Beata, Lutowski, Zbigniew, Flizikowski, Adam, Oyerinde, Olutayo Oyeyemi
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 14.07.2021
• Subjects: Coefficients; Graph theory; Graphs; Mathematical analysis; Network topologies; Nodes; Shortest-path problems; Simulation; Unevenness
• ISSN: 2079-9292; 2079-9292
• DOI: 10.3390/electronics10141684

This paper discusses an evaluation method of transmission properties of networks described with regular graphs (Reference Graphs) using unevenness coefficients. The first part of the paper offers generic information about describing network topology via graphs. The terms ‘chord graph’ and ‘Reference Graph’, which is a special form of a regular graph, are defined. The operating principle of a basic tool used for testing the network’s transmission properties is discussed. The next part consists of a description of the searching procedure of the shortest paths connecting any two nodes of a graph and the method determining the number of uses of individual graph edges. The analysis shows that using particular edges of a graph depends on two factors: their total number in minimum length paths and their total number in parallel paths connecting the graph nodes. The latter makes it possible to define an unevenness coefficient. The calculated values of the unevenness coefficients can be used to evaluate the transmission properties of networks and to control the distribution of transmission resources.