2) Which layout seems most suitable?

twopi, fdp and neato work well.

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3) Calculate the reverse graph.

FR = F.reverse()

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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.

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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.

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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.