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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: ki II¿ = Ꮓ - 1 N(t-1) with Z (k-1) j=1 where k; is the degree of node i, and N(t -1) is the number of nodes in the network at time t - 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).

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: ki II¿ = Ꮓ - 1 N(t-1) with Z (k-1) j=1 where k; is the degree of node i, and N(t -1) is the number of nodes in the network at time t - 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).

Elements Of Modern Algebra
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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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: ki II¿ = Ꮓ - 1 N(t-1) with Z (k-1) j=1 where k; is the degree of node i, and N(t -1) is the number of nodes in the network at time t - 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).
Transcribed Image Text: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: ki II¿ = Ꮓ - 1 N(t-1) with Z (k-1) j=1 where k; is the degree of node i, and N(t -1) is the number of nodes in the network at time t - 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).
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