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. 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.
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. 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.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 7E
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