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) (B) Assume that π(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.

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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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)
(B) Assume that
π(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.
Transcribed Image Text:(B) Assume that π(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.
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