Depending on what seems more relevant in your graph, pick one of the following local notions :

• Decay centrality

 • Betweenness centrality

 • Closeness centrality 

• Clustering 

1) Provide a code computing the given centrality using basic functions of networks (you are not allowed to use direct functions of network). 

2) Discuss why you picked this measure and who is the most central in your network based on your choice. 

3) Provide the cumulative distribution for this centrality and give a graphical representation of your graph (log-log, log, or normal representation as you think it is more relevant)

1) Write a function to compute the PageRank of the nodes in a graph (you are not allowed to use built-in functions from NetworkX).

 2) Run it on your graph using α = 0.15, save the total number of iterations, and check that your function returns the same results (in terms of the scores) as the built-in function from NetworkX. 

3) Identify the node with the highest PageRank, compare it with the one you got from week 3, and give an interpretation of the possible difference. 

4) Provide the cumulative distribution, compare it with the one you got from week 3 (the above questions), and comment on the results.

 5) Optional: Re-run the PageRank using α = 0.5, save the total number of iterations, compare with the results (in terms of both the number of iterations and the cumulative distribution) obtained for α = 0.15, and comment.