The Erdős–Rényi Algorithm from the Point of View of Category Theory. \(\user2{P }\) - Giant Component of an Algebraic System

The chapter presents the following results in an overview order: In Sect. 8.5 Erdős–Rényi Model. \(P\) - Giant Component in Algebraic Systems the main outlined points are: with respect to the main operations and predicates of the algebraic system. In Sect. 8.5.4 we consider the inverse Erdős–Rényi algorithm, inverse second Erdős–Rényi random graph model \(IG\left( {n,p} \right)\) . The first question arises here is the question of a fisical sence of such approximation. The inverse Erdős–Rényi algorithm is an analogue of linear regression, i.e., in essence, it is an approximation of \(P\) -a giant component of an algebraic system by an algebraic system with property \(P\) .