The Relative Isolation Probability of a Vertex in a Multiple-Source Edge-Weighted Graph

• Main Authors: Tan, Renzo Roel P, See, Kyle Stephen S, Kawahara, Jun, Ikeda, Kazushi, De Jesus, Richard, Garciano, Lessandro Estelito, Garciano, Agnes
• Format: text
• Published: Archīum Ateneo 2022
• Subjects: frontier-based search; graph measure; Monte Carlo method; probability of relative isolation; zero-suppressed binary decision diagram; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/184; https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1188&context=mathematics-faculty-pubs
• Institution: Ateneo De Manila University

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.