System flow centrality index for evaluating the influence of a given system element in a network graph

This paper introduces a novel System Flow Centrality (SFC) index for evaluating node importance in network graphs, with a specific focus on system architecture analysis. Unlike traditional centrality measures such as betweenness centrality (BC), the SFC index considers all system paths and cycles, providing a more comprehensive assessment of a node's influence within the network. We present both a basic SFC algorithm and an enhanced version that incorporates system element classification, allowing for more nuanced analysis of component properties. The proposed index is validated through application to various network topologies, including common IEEE bus system configurations and a real-world medical motor driver architecture. Comparative analysis with established centrality measures demonstrates the SFC index's superior performance in identifying critical nodes, particularly in complex and asymmetric network structures. The SFC index shows promise as a valuable tool for multidisciplinary project teams, offering potential benefits in risk assessment, resource allocation, quality management optimization, and decision-making processes across diverse applications. This research contributes to the growing body of knowledge on network analysis and system architecture evaluation, providing a more accurate and system-oriented approach to quantifying node importance in complex networks.