Consider the following growing network model in which each node i isassigned 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 hasinitially 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 existingnode of the network chosen with probability II; given bywhereZ=Ili=aiZ'Σ aj.j=1,...,N(t−1) (B) Assume thatπ(a) = {and that Z ~āt.1,1 for a =0 for a 1,Derive the degree distribution P(k) of the network for large times, i.e.t>1, in the mean-field approximation.

In the mean-field approximation:(A) The expected degree of any node at any time is approximately…

Answered: Consider the following growing network…

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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