Erdős–Rényi Models and Neutrosophic Sets

Abstract

Networks comprise a vast array of diverse entities, including organizations, computers, airports, and more. The elements are interconnected either physically (e.g., through cables or microwaves) or mentally, when they pertain to ideas or concepts. In the broadest context, the linkages exhibit no discernible pattern. Graphs are mathematical constructs utilized to represent networks and analyze their characteristics. A random graph is one in which a stochastic process dictates the existence of an edge between two vertices. An Erdős–Rényi model is a framework for generating random graphs or examining the evolution of a random graph. Substituting likelihood with plausibility results in a fundamentally distinct framework that can be mathematically characterized using fuzzy graphs. In addition, we gain far more flexibility by adding a measure of the opposite of plausibility and a measure of indeterminacy. This naturally leads to a reinterpretation of established concepts and ideas and the framework of neutrosophic set theory.