2) Which layout seems most suitable? twopi, fdp and neato work well. ----------------------------------------- 3) Calculate the reverse graph. FR = F.reverse() ----------------------------------------- 4) Calculate the PageRank of the reverse graph. pgr = pagerank(FR) for item in sorted(pgr.iteritems(), key=itemgetter(1), reverse=True): print item Why is Claire high in F and low in the reverse graph? Claire is called "friend" by 3 people including Helen who is top ranked in F. Claire only calls one person "friend" herself (as does Richard). In FR: because Richards' friend Sue is higher ranked than Claire's friend Helen, Claire is ranked below Richard. Why are Helen and Sue highly ranked in F and in the reverse graph? They both have many friends and are called "friend" by many people. ----------------------------------------- 5) Determine whether the friends graph is a small-world network FU = F.to_undirected() average_shortest_path_length(FU) average_clustering(FU) FR = gnm_random_graph(FU.number_of_nodes(), FU.number_of_edges()) average_clustering(FR) The average shortest path is 1.55. This means that on average it takes less than 2 steps to get from a node to any other node. This proves the small-world effect. The average clustering coefficient (0.55) is larger than for a random graph. Thus, it is a small-world network. ----------------------------------------- 6) Can you figure out how many hands you shook and how many hands your girlfriend/boyfriend shook? Because each person gives a different answer, the answers are 0, 1, 2, 3, 4, 5, 6. Start drawing a graph by placing 8 nodes in a circle. Draw 6 edges connected to a single node (the person with 6 handshakes). The girlfriend/boyfriend of this person, must be the one who shook 0 hands. Pick another node to be the one with 5 handshakes, it doesn't matter which one. The girlfriend/boyfriend of this person, must be the one who shook 1 hand. Pick another node to be the one with 4 handshakes, it doesn't matter which one. The girlfriend/boyfriend of this person, must be the one who shook 2 hands. The remaining two nodes both have 3 edges. These must be you and your girlfriend/boyfriend.