Which of the following statements isare TRUE? As we increase the value of the exponent a in the nonlinear Preferential Attachment I k ck, where c is a positive constant, the following happens:
A: The maximum degree is expected to reduce.
B: The degree variance is expected to increase.
C: The degree distribution is expected to be less skewed
D: The network is expected to become denser
In the analysis of the PA model, we derived a recurrent relationship for the probability of degreem nodes:
recall that m is the number of edges we add with each new node
N 1 Pm t 1 N Pm t 1 m2 Pm t
We used this expression to show that, as t infinity, this probability becomes Pm 2 m2.
Suppose that we analyze a different model of network growth in which we have the following recurrent expression for the probability of degreem nodes:
N 2 Pm t 1 N Pm t 2 m2 Pm t
Explanation of the model: Instead of one, we add two nodes into the network at each time step.
We attach the first node to the network following the rules of PA model, while we connect the second node to all the neighbors of the first node.
Give the formulae for Pm for this modified model.
Question 3
Select the right choice about the network generated by the linkcopy model.
1. When p approaches 1, the network has a degree distribution similar to that of Gn.p networks here p in Gn,p is independent of the p we used in linkcopy model.
2. When p 12, the linkcopy network is identical to the network generated by a PA
model. Select
3. When g approaches 0, the network has a powerlaw distribution with exponent 2.
4 When g 12, the network has a powerlaw distribution with exponent 3
Which of the following statements is TRUE about networks generated with HRG model with dendrogram D?
A:For the purpose of generating a network with hubs, we can do so by setting p. to high values for nodes in D closer to the root.
B: For the purpose of generating a network with strong community structures, we can do so by set p, to high values for all internal nodes in D that are LCA of nodes in the same community.
C: The HR model cannot generate networks that are unconnected, because of the tree structure of D.
D: For the purpose of generating a network with strong clustering property, we must have the lower closer to leaves internal nodes in D to have higher values of p, than the higher nodes in D
We know that the GirvanNewman GN model, the LF method, and the Stochastic Block Model SBM are three models that can generate networks with community structure. Select the right statement about the comparison between these models?
1. SBM can generate any network that GN model can generate.
2. LFR can generate any network that SBM can generate. Select
3. SBM can generate any network that LFR can generate. Select
4. All three models can be tuned to generate networks without community structure.