4. As we have seen, if a 1wertex in a random graph has (at least] one edge connecting it to the giant component then it is itself in the giant component. 0n the other handI if a 1vertex has at least two connections to the giant component then it is in the giant bicmpoaent. (a) Consider a random graph G (11,31) with average degree c, and let S be the fraction of the network lled by the giant component. Show.r that the probability of a vertex having no connections at all to the giant component is {Fr-S in the limit of large n. (b) Show that the probability' of exactly one connection to the giant componentno more and no lessis (eES in the limit of large n. {c} Hence show that the fraction T of the network lled by the giant hicomponent is T = 1 [1 + CS)_'S