=Consider the following model to grow simple networks. At time t = 1 we start with acomplete network with no 6 nodes. At each time step t> 1 a new node is added tothe network. The node arrives together with m = 2 new links, which are connected tom = 2 different nodes already present in the network. The probability II; that a newlink is connected to node i is:ki – 1II¿ZN(t-1)with Z = (k; - 1)j=1where k¿ is the degree of node i, and N(t − 1) is the number of nodes in the network attime 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 afunction of time t.(b) What is the average node degree (k) at time t? What is the average node degreein the limit t→ ∞?(c) Write down the differential equation governing the time evolution of the degree kiof node i for t≫ 1 in the mean-field approximation. Solve this equation with theinitial condition k¿(t;) = m, where t¿ is the time of arrival of node i.

Solution Let's break down each part of your question:(a) To find expressions for N(t) and L(t), we…

Answered: = Consider the following model to grow…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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