Consider the following model to grow simple networks. At time t = 1 we start with a complete network with no = 6 nodes. At each time step t > 1 a new node is added to the network. The node arrives together with m = 2 new links, which are connected to m = 2 different nodes already present in the network. The probability II, that a new link is connected to node i is: N(t-1) II¿ = ki - 1 Ꮓ with Z=(k-1) j=1 where ki is the degree of node i, and N(t - 1) is the number of nodes in the network at timet - 1. (f) Suppose now that you iterate the growing process for a finite number of time steps, until you produce a final network with N = 106 nodes (and a minimum degree m2). Denote as K the natural cutoff in the network. Treating the degree k as a continuous variable, evaluate the natural cutoff K, the normalisation constant in the degree distribution, the average degree (k), and (k2). (g) Calculate the probability of finding a node with 1000 links in the network obtained in point (f). Calculate the probability of finding a node with 1000 links in a Erdös-Rényi random graphs with the same number of nodes and links as in the network obtained in point (f).