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Provide the mean-field solution of the model by considering the following two points. (A) Assume that Zāt, where a indicates the average of a over the distribution π(a). Derive the time evolution ki = ki(t) of the expected degree ki of a node i in the mean-field approximation.

Provide the mean-field solution of the model by considering the following two points. (A) Assume that Zāt, where a indicates the average of a over the distribution π(a). Derive the time evolution ki = ki(t) of the expected degree ki of a node i 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 π(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 of the network chosen with probability II; given by where Z = Ili = ai Z' Σ aj. j=1,...,N(t−1)
Transcribed Image Text:Consider the following growing network model in which each node i is assigned an attractiveness a¿ € N+ drawn from a distribution π(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 of the network chosen with probability II; given by where Z = Ili = ai Z' Σ aj. j=1,...,N(t−1)
Provide the mean-field solution of the model by considering the following two points. (A) Assume that Zāt, where ā indicates the average of a over the distribution (a). Derive the time evolution ki = ki (t) of the expected degree k; of a node i in the mean-field approximation.
Transcribed Image Text:Provide the mean-field solution of the model by considering the following two points. (A) Assume that Zāt, where ā indicates the average of a over the distribution (a). Derive the time evolution ki = ki (t) of the expected degree k; of a node i in the mean-field approximation.
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