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The study of random graphs emerged as a distinct field with the influential paper by Erd¨os and R´enyi, and it is widely regarded as one of the most important areas within graph theory. Different models of random graphs exist, each characterized by its unique probability distribution for generating graphs. One approach involves starting with individual vertices and randomly adding edges between them. Various random graph models generate distinct probability distributions for the resulting graphs. One of the frequently studied models is denoted as G(n, p), encompassing all labeled graphs with n vertices. In this model, each possible edge appears independently with a probability of 0 ⩽ p ⩽ 1. Another natural model of random graphs is denoted as G(n, m), which represents the probability space of all labeled graphs with n vertices and exactly m edges.