(e) Consider the case a = 0 and the case a = 1. Calculate C and derive the degree distribution in the mean-field approximation. (f) For which values of a E [0,1] is the network scale-free? 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.
(e) Consider the case a = 0 and the case a = 1. Calculate C and derive the degree distribution in the mean-field approximation. (f) For which values of a E [0,1] is the network scale-free? 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
Related questions
Question
![(e) Consider the case a = 0 and the case a = 1. Calculate C and derive the degree
distribution in the mean-field approximation.
(f) For which values of a E [0,1] is the network scale-free?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37f6c14e-1e03-4c74-ad14-0ec9447f468a%2F6d541556-36f7-40dc-a4e6-107d7d62b8ba%2F8nrgcm8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(e) Consider the case a = 0 and the case a = 1. Calculate C and derive the degree
distribution in the mean-field approximation.
(f) For which values of a E [0,1] is the network scale-free?
![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%2F6d541556-36f7-40dc-a4e6-107d7d62b8ba%2Fo3i751d_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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