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...

Considering the definitions of Network Flow , please select the INCORRECT affirmation below: A.  There are two types of special nodes, Source and Sink. B. The flow-conservation property says that the total flow  into a node other than the source or sink must equal the total flow out of that  node (flow in equals flow out). C. Between two nodes ( A and B ), links flowing in opposite directions (antiparallel edges) are allowed ( A to B , and B to A ). D. Multiple edges (Parallel edges, i.e., same directions) between two nodes are allowed (Same start and end nodes). E. None of the above. Original idea by: Felipe Crispim da Rocha Salvagnini

Suppose you start analysing the evolution of a real-network that you are interested in. When studying its growth, you identify that it can be mapped as a copying model . The current state of the network has 2018 nodes and 2930 links, and a new node has a probability of 0.137 to select randomly a target node u . What are the preferential attachment values for this new node to connect with nodes of degree 13 and 21 ( Rounding to Three Decimal Places )? A. Π(13) : 0.003, Π(21) : 0.005 B.  Π(13) : 0.002, Π(21) : 0.003 C.  Π(13) : 0.002, Π(21) : 0.004 D.  Π(13) : 0.003, Π(21) : 0.001 E. None of the above. Original idea by: Felipe Crispim da Rocha Salvagnini

 Given the following reverse graph below, alongside its reverse order of finishing times (DFS starting at node 1), please, identify the number of strongly connected components in the original graph, using the Kosaraju-Sharir’s algorithm: A. 3 B. 4 C.  2 D.  5 E. None of the above. Original idea by: Felipe Crispim da Rocha Salvagnini