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 m = = 2 new links, which are connected to 2 different nodes already present in the network. The probability II; that a new link is connected to node i is: Π = ki Z N(t-1) — 1 with Z = Σ (ky - 1) j=1 where ki is the degree of node i, and N(t − 1) is the number of nodes in the network at time t — 1. - (a) Find an expression for the number of nodes, N(t), and the number of links, L(t), in the network as a function of time t. Find an expression for the value of Z as a function of time t. (b) What is the average node degree (k) at time t? What is the average node degree in the limit t→ ∞?