(c) Derive the time evolution k₁ = ki(t) of the expected degree ki of a node i for t≫ 1 in the mean-field, continuous approximation. (d) Consider the case a = (0, 1) and assume that we know the value of C. Derive the degree distribution in the mean-field approximation. Consider the following model to grow simple networks. At time t = 1 the network is formed by no = 3 nodes and mo= 1 link. At each time step t> 1 a new node is added to the network. The node arrives together with 3 new links, which are connected to 3 different nodes already present in the network. The probability II; that a new link is connected to node j is: k II; = 57 where k; indicates the degree of node j, a € [0,1] and Z = 1. Assume that for t> 1 we can approximate Z as ZCt where C is a time-independent constant.
(c) Derive the time evolution k₁ = ki(t) of the expected degree ki of a node i for t≫ 1 in the mean-field, continuous approximation. (d) Consider the case a = (0, 1) and assume that we know the value of C. Derive the degree distribution in the mean-field approximation. Consider the following model to grow simple networks. At time t = 1 the network is formed by no = 3 nodes and mo= 1 link. At each time step t> 1 a new node is added to the network. The node arrives together with 3 new links, which are connected to 3 different nodes already present in the network. The probability II; that a new link is connected to node j is: k II; = 57 where k; indicates the degree of node j, a € [0,1] and Z = 1. Assume that for t> 1 we can approximate Z as ZCt where C is a time-independent constant.
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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Transcribed Image Text:(c) Derive the time evolution k₁ = ki(t) of the expected degree ki of a node i for t≫ 1
in the mean-field, continuous approximation.
(d) Consider the case a = (0, 1) and assume that we know the value of C. Derive the
degree distribution in the mean-field approximation.
![Consider the following model to grow simple networks. At time t = 1 the network is
formed by no = 3 nodes and mo= 1 link. At each time step t> 1 a new node is added
to the network. The node arrives together with 3 new links, which are connected to 3
different nodes already present in the network. The probability II; that a new link is
connected to node j is:
k
II; =
57
where k; indicates the degree of node j, a € [0,1] and Z = 1. Assume that for
t> 1 we can approximate Z as ZCt where C is a time-independent constant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37f6c14e-1e03-4c74-ad14-0ec9447f468a%2Fc57c3925-7977-4194-a0fa-32e2ebf5bea8%2Fiqgpyjn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following model to grow simple networks. At time t = 1 the network is
formed by no = 3 nodes and mo= 1 link. At each time step t> 1 a new node is added
to the network. The node arrives together with 3 new links, which are connected to 3
different nodes already present in the network. The probability II; that a new link is
connected to node j is:
k
II; =
57
where k; indicates the degree of node j, a € [0,1] and Z = 1. Assume that for
t> 1 we can approximate Z as ZCt where C is a time-independent constant.
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