The degree distribution of a network has the following functional form:Pk = Cak,Where a < 1 is a constant, and k ≥ 1 is the degree.a.Find out the value of C.b. Find out its probability generating function go(z) in compact form.C. Find out the corresponding generating function g₁(z) for its excess degreedistribution in compact form.d. Find out the probability that a node in this network has zero 2nd neighbors.condition for a such that a giant component is present.e.Find out thef.When 1 -fraction of nodes are randomly removed, find out the criticalvalue of when giant cluster emerges.g. What is the size of the giant cluster if it exists?

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The degree distribution of a network has the following functional form: Pk = Cak, Where a < 1 is a constant, and k ≥ 1 is the degree. a. Find out the value of C. b. Find out its probability generating function go (z) in compact form.

The degree distribution of a network has the following functional form: Pk = Cak, Where a < 1 is a constant, and k ≥ 1 is the degree. a. Find out the value of C. b. Find out its probability generating function go (z) in compact form.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy

Problem 8EA

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Question

The degree distribution of a network has the following functional form:
Pk = Cak,
Where a < 1 is a constant, and k ≥ 1 is the degree.
a.
Find out the value of C.
b. Find out its probability generating function go(z) in compact form.
C. Find out the corresponding generating function g₁(z) for its excess degree
distribution in compact form.
d. Find out the probability that a node in this network has zero 2nd neighbors.
condition for a such that a giant component is present.
e.
Find out the
f.
When 1 -
fraction of nodes are randomly removed, find out the critical
value of when giant cluster emerges.
g. What is the size of the giant cluster if it exists?

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