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(B) Assume that (a) = { 1 for a 1, 0 for a 1, and that Zāt. Derive the degree distribution P(k) of the network for large times, i.e. t>1, in the mean-field approximation.

(B) Assume that (a) = { 1 for a 1, 0 for a 1, and that Zāt. Derive the degree distribution P(k) of the network for large times, i.e. t>1, in the mean-field approximation.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Consider the following growing network model in which each node i is assigned an attractiveness a € N+ drawn from a distribution (a). Let N(t) denote the total number of nodes at time t. At time t = 1 the network is formed by two nodes joined by a link. At every time step a new node joins the network. Every new node has initially a single link that connects it to the rest of the network. - At every time step t the link of the new node is attached to an existing node i of the network chosen with probability II; given by where II₁ = Ꮓ Z = Σ aj. j=1,...,N(t-1) Provide the mean-field solution of the model by considering the following two points. (B) Assume that 7(a) = { 1 for a 1, 0 for a 1, = and that Zāt. Derive the degree distribution P(k) of the network for large times, i.e. t>1, in the mean-field approximation.
Transcribed Image Text:Consider the following growing network model in which each node i is assigned an attractiveness a € N+ drawn from a distribution (a). Let N(t) denote the total number of nodes at time t. At time t = 1 the network is formed by two nodes joined by a link. At every time step a new node joins the network. Every new node has initially a single link that connects it to the rest of the network. - At every time step t the link of the new node is attached to an existing node i of the network chosen with probability II; given by where II₁ = Ꮓ Z = Σ aj. j=1,...,N(t-1) Provide the mean-field solution of the model by considering the following two points. (B) Assume that 7(a) = { 1 for a 1, 0 for a 1, = and that Zāt. Derive the degree distribution P(k) of the network for large times, i.e. t>1, in the mean-field approximation.
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