#### Document Type

Article

#### Publication Date

2-24-2022

#### Abstract

Various measures that characterize graphs exist in literature. Insights into the properties of a graph as a whole and its components are revealed largely through graph measures, also called graph metrics. In seeking to interpret a consequential edge metric from a vertex-centric perspective, the paper advances an original measure – the relative isolation probability of a vertex. Concisely, the probability of relative isolation pertains to the likelihood of a vertex to be disconnected from all designated source vertices in a graph with probability-weighted edges. A two-step algorithm for efficient calculation is presented and evaluated. Contained within the procedure is a Monte Carlo simulation and the use of a compact data structure called the zero-suppressed binary decision diagram, efficiently constructed through the frontier-based search. The novel measure is then computed for a diverse set of graphs, serving as benchmark for the proposed method. In closing, case studies on real-world networks are performed to ensure the consistency of the experimental with the actual.

#### Recommended Citation

Tan, R. R. P., See, K. S. S., Kawahara, J., Ikeda, K., de Jesus, R. M., Garciano, L. E. O., & Garciano, A. D. (2022). The relative isolation probability of a vertex in a multiple-source edge-weighted graph. Engineering Letters, 30(1), 117-130. http://www.engineeringletters.com/issues_v30/issue_1/index.html