10.2 Suppose that a network has a degree distribution that follows the exponential (or geometric) form pk ???? Cak, where C and a are positive constants and a < 1.

1. a) Assuming the distribution is properly normalized, find C as a function of a.
2. b) Calculate the fraction P of nodes that have degree k or greater.
3. c) Calculate the fraction W of ends of edges that are attached to nodes of degree k orgreater.
4. d) Hence show that the Lorenz curve—the equivalent of Eq. (10.24) for this degreedistribution—is given byW ???? P − 1 − 1/a P log P.log a
5. e) Show that the value of W is greater than one for some values of P in the range0 ≤ P ≤ 1. What is the meaning of these “unphysical” values?

Please give me the steps that solving this problem. Thanks!