Deep Reach Centrality: An Innovative Network Centrality Metric Grounded in Distance and Degree, with Its Performance Analysis Applied to the SARS-CoV-2 Protein–protein Interaction Network

Centrality measures are widely valued in graph-related data applications, as they play a crucial role in predicting highly influential nodes. This enables subsequent processes to be efficiently formulated, guided by the influence and directionality of these central nodes. Centrality measures have practical utility across diverse fields and situations where the analysis of networks, the assessment of node significance, and the evaluation of information propagation are critical concerns. These applications span a range of domains, including Social Network Analysis, Transportation and Infrastructure Planning, as well as Biology and Bioinformatics. The computation of a node’s centrality value using the proposed centrality measure involves a comprehensive approach. It doesn’t solely rely on finding the shortest paths to all other nodes but also takes into account whether nodes with high degrees can be reached in fewer hops. In this regard, the proposed method identifies the most influential node by considering the attributes of neighborhoods with higher degrees, reachable within a shorter hop distance to access all other nodes in the graph. Efficiency and comparative analysis were conducted on the proposed deep version of reach centrality in conjunction with 13 existing centrality measures within SARS-CoV-2 protein–protein interaction networks. The Pearson correlation coefficient was employed to assess the degree of similarity and dissimilarity between the proposed centrality measure and other existing measures. To reduce the dimensionality of the centrality values and identify the most influential measure, an unsupervised learning technique known as Principal Component Analysis (PCA) was applied. For evaluating the cluster tendency of the data, both the silhouette method and the elbow method were utilized. Furthermore, the K-means algorithm was implemented to cluster the centrality measures based on their responses within SARS-CoV-2 networks. These analyses yielded significant results, providing evidence for the effectiveness of the proposed measure.