Question 1: Considering a random graph G(n, p) , which of the following statements correctly describes the properties that emerge near the critical threshold of connectivity as the probability p increases? Options: 1) The emergence of a giant component, where a significant number of nodes connect to form a large connected component. 2) The critical threshold of connectivity occurs approximately when p is equal to log(n)/n. 3) Before the connectivity threshold, the graph is mainly composed of many small and isolated components. 4) After the connectivity threshold, all nodes in the graph become fully connected, forming a complete graph. 5) Upon reaching the critical threshold, the average number of edges in the graph follows a normal distribution centered at n . Correct Answers: a) 1, 2, and 3 are correct. b) 2 and 4 are correct. c) 1 and 5 are correct. d) 3, 4, and 5 are correct. Question 2: Given a random graph G(n, p) in the Erdős–Rényi model, what is the main theoretical reason w