Felipe Crispim

 Hi professor, for this week quiz, I have refactored the network flow question .

In simple networks (No multi links), there is a conflict between the scale-free property and degree correlations. This conflict arises because in some scale-free and random networks, with degree correlation, may be predicted more than one link between two sufficiently large hubs (As a simple network does not allow them, we have a conflict between degree correlations and the scale-free property). Consider the following statements: I - By comparing the structural cutoff ( ks ) with the natural cutoff ( kmax ) we can distinguish between two network regimes ( No Structural Cutoff  and  Structural Disassortativity )  II - Would be expected multiple links for nodes whose degrees are below a given degree threshold ( ks ). III - Is possible to have a scale-free network that is neutral or assortative, if we remove all hubs with degrees larger than ks . IV - Under the Structural Disassortativity regime, the network would have more links between its hubs than the predicted value. C...

Since the Barabási-Albert model has well-known limitations, some extensions were proposed to it. Those extensions capture a range of phenomena known to shape the topology of real networks. With those extensions in mind, analyze the following statements: I.  Initial Attractiveness:  adds a constant  A  to the preferential attachment function, inducing a small-degree saturation for  k < A . It enhances the probability that a new node links to a small-degree node. II.  Internal links:  enables a link between pre-existing nodes to arrive. III.  Node deletion:  enables the deletion of nodes with a rate  r . If  r=1 , the generated network keeps its scale-free nature. IV.  Accelerated Growth:  enables the evolution of a network where the number of links grows faster than N . V.  Aging:   modifies the preferential attachment function to consider the node's age. There is a tunable parameter,  v , which contr...