Bond Additive Molecular Descriptors of Interconnection Networks

In this article, a graph-theoretical framework is employed to analyze the structural
characteristics of key interconnection networks - butterfly, benes, and mesh-derived
networks (MDNs): MDN1 and MDN2, through the application of bond-additive
molecular descriptors, particularly the Adriatic indices. The aim is to quantitatively
assess the efficiency and strength of these networks using tools from chemical graph
theory. Each network is represented as a graph, and various forms of Adriatic indices
are computed analytically, incorporating different edge-weighting schemes. These
indices effectively characterize topological features such as connectivity, regularity,
redundancy, and fault tolerance. The findings indicate that butterfly and benes networks
exhibit high regularity with limited redundancy, whereas MDNs demonstrate enhanced
fault tolerance and scalability. This consistent descriptor-based analysis facilitates
comparative evaluation of network architectures across different sizes and complexities.
The approach introduced in this study bridges molecular descriptor theory with
interconnection network analysis, offering both theoretical and practical insights