Consider the following growing network model in which each node i is assigned an attractiveness a € N+ drawn from a distribution (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 i of the network chosen with probability II, given by II₁ ai = Z where Z = Σ aj. j=1,...,N(t−1) Consider the following growing network model in which each node i is assigned an attractiveness a € N+ drawn from a distribution (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 i of the network chosen with probability II, given by II₁ ai = Z where Z = Σ aj. j=1,...,N(t−1)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

Provide the mean-field solution of the model by considering the following point.

Consider the following growing network model in which each node i is
assigned an attractiveness a € N+ drawn from a distribution (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 i of the network chosen with probability II, given by
II₁
ai
= Z
where
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 (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 i of the network chosen with probability II, given by II₁ ai = Z where Z = Σ aj. j=1,...,N(t−1)
Consider the following growing network model in which each node i is
assigned an attractiveness a € N+ drawn from a distribution (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 i of the network chosen with probability II, given by
II₁
ai
= Z
where
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 (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 i of the network chosen with probability II, given by II₁ ai = Z where Z = Σ aj. j=1,...,N(t−1)
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,