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= (f) Suppose now that you iterate the growing process for a finite number of time steps, until you produce a final network with N 106 nodes (and a minimum degree m = 2). Denote as K the natural cutoff in the network. Treating the degree k as a continuous variable, evaluate the natural cutoff K, the normalisation constant in the degree distribution, the average degree (k), and (k2). (g) Calculate the probability of finding a node with 1000 links in the network obtained in point (f). Calculate the probability of finding a node with 1000 links in a Erdös-Rènyi random graphs with the same number of nodes and links as in the network obtained in point (f). Consider the following model to grow simple networks. At time t = 1 we start with a complete network with no = 6 nodes. At each time step t> 1 a new node is added to the network. The node arrives together with m = = 2 new links, which are connected to 2 different nodes already present in the network. The probability II; that a new link is connected to node i is: m = N(t-1) Π ki - 1 Z with Z = Σ (ky - 1) j=1 I where ki is the degree of node i, and N(t - 1) is the number of nodes in the network at time t-1.

= (f) Suppose now that you iterate the growing process for a finite number of time steps, until you produce a final network with N 106 nodes (and a minimum degree m = 2). Denote as K the natural cutoff in the network. Treating the degree k as a continuous variable, evaluate the natural cutoff K, the normalisation constant in the degree distribution, the average degree (k), and (k2). (g) Calculate the probability of finding a node with 1000 links in the network obtained in point (f). Calculate the probability of finding a node with 1000 links in a Erdös-Rènyi random graphs with the same number of nodes and links as in the network obtained in point (f). Consider the following model to grow simple networks. At time t = 1 we start with a complete network with no = 6 nodes. At each time step t> 1 a new node is added to the network. The node arrives together with m = = 2 new links, which are connected to 2 different nodes already present in the network. The probability II; that a new link is connected to node i is: m = N(t-1) Π ki - 1 Z with Z = Σ (ky - 1) j=1 I where ki is the degree of node i, and N(t - 1) is the number of nodes in the network at time t-1.

Advanced Engineering Mathematics
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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= (f) Suppose now that you iterate the growing process for a finite number of time steps, until you produce a final network with N 106 nodes (and a minimum degree m = 2). Denote as K the natural cutoff in the network. Treating the degree k as a continuous variable, evaluate the natural cutoff K, the normalisation constant in the degree distribution, the average degree (k), and (k2). (g) Calculate the probability of finding a node with 1000 links in the network obtained in point (f). Calculate the probability of finding a node with 1000 links in a Erdös-Rènyi random graphs with the same number of nodes and links as in the network obtained in point (f).
Transcribed Image Text:= (f) Suppose now that you iterate the growing process for a finite number of time steps, until you produce a final network with N 106 nodes (and a minimum degree m = 2). Denote as K the natural cutoff in the network. Treating the degree k as a continuous variable, evaluate the natural cutoff K, the normalisation constant in the degree distribution, the average degree (k), and (k2). (g) Calculate the probability of finding a node with 1000 links in the network obtained in point (f). Calculate the probability of finding a node with 1000 links in a Erdös-Rènyi random graphs with the same number of nodes and links as in the network obtained in point (f).
Consider the following model to grow simple networks. At time t = 1 we start with a complete network with no = 6 nodes. At each time step t> 1 a new node is added to the network. The node arrives together with m = = 2 new links, which are connected to 2 different nodes already present in the network. The probability II; that a new link is connected to node i is: m = N(t-1) Π ki - 1 Z with Z = Σ (ky - 1) j=1 I where ki is the degree of node i, and N(t - 1) is the number of nodes in the network at time t-1.
Transcribed Image Text:Consider the following model to grow simple networks. At time t = 1 we start with a complete network with no = 6 nodes. At each time step t> 1 a new node is added to the network. The node arrives together with m = = 2 new links, which are connected to 2 different nodes already present in the network. The probability II; that a new link is connected to node i is: m = N(t-1) Π ki - 1 Z with Z = Σ (ky - 1) j=1 I where ki is the degree of node i, and N(t - 1) is the number of nodes in the network at time t-1.
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