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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¿ = Z - 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. (b) What is the average node degree (k) at time t? What is the average node degree in the limit t→ ∞o?

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¿ = Z - 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. (b) What is the average node degree (k) at time t? What is the average node degree in the limit t→ ∞o?

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¿ = Z - 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. (b) What is the average node degree (k) at time t? What is the average node degree in the limit t→ ∞o?
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¿ = Z - 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. (b) What is the average node degree (k) at time t? What is the average node degree in the limit t→ ∞o?
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