Algoritmos em Grafos - Alexandre

Classify the alternatives as true or false, regarding degree correlation properties in networks: I: For assortative networks, the transition to a giant component takes longer, as hubs preferentially connect to each other. II: For a disassortative network, the degree correlation function knn (k) increases with k. III: Structural disassortativity is a phenomenon observed in scale-free networks where  γ < 3 , which arises because the network lacks a sufficient number of links to connect the large hubs in a neutral way. IV: Assortative networks have a shorter average path length than neutral networks, but also a larger network diameter. A) T-F-T-T B) T-F-F-F C) F-F-T-T D) T-F-F-T E) None of the above Original idea by: Alexandre Petrachini

 A friend of yours has published a pioneering research paper in a niche area, and it has gathered several citations from other researchers. The directed graph below shows the citation relationships among papers in this area. Your friend is extremely happy with the results, given that his Paper A is already the most influent paper in the network, with an incoming degree of 4. Curious, with your knowledge on network science, you want to understand what the probability of a new paper is citing paper A.  You are happy with rough approximations, so you frame this problem using a copying model of a directed network. With the probability of linking uniformly at random to an existing paper of p = 0.4, and the probability of copying of a link from a random citation of 1 - p, what is the probability of a new paper connecting to paper A? Round to two decimal places. a) 0.1 b) 0.20 c) 0.29 d) 0.21 e) None of the above Original idea by: Alexandre Petrachini