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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: N(t-1) II₁ = ki - 1 Z == 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 timet - 1. (e) Write down the master equation of the model, i.e. the equation that describes the evolution of the average number N(t) of nodes that at time t have degree k.

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) II₁ = ki - 1 Z == 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 timet - 1. (e) Write down the master equation of the model, i.e. the equation that describes the evolution of the average number N(t) of nodes that at time t have degree k.

Advanced Engineering Mathematics
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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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) II₁ = ki - 1 Z == 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 timet - 1. (e) Write down the master equation of the model, i.e. the equation that describes the evolution of the average number N(t) of nodes that at time t have degree k.
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: N(t-1) II₁ = ki - 1 Z == 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 timet - 1. (e) Write down the master equation of the model, i.e. the equation that describes the evolution of the average number N(t) of nodes that at time t have degree k.
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