3 Consider a configuration model network that has vertices of degree 1, 2, and 3 only, in fractions p 1, p 2, and p 3, respectively.

16.3 Consider a configuration model network that has vertices of degree 1, 2, and 3 only, in

fractions p1, p2, and p3, respectively.       

a. Find the value of the critical vertex occupation probability φc at which site percolation takes

place on the network.

b. Show that there is no giant cluster for any value of the occupation probability φ if p1 > 3p3.

Why does this result not depend on p2?

c. Find the size of the giant cluster as a function of φ. (Hint: you may find it useful to

remember that u = 1 is always a solution of the equation u = 1 − φ + φg1 (u).)