Design a parallel algorithm that will process a graph of size n and calculates the closeness centrality and$/$or betweenness centrality for each node. You will implement this algorithm using Message Passage Interface $($MPI$)$ libraries for Python$1.$

Output: The first processor $($ID$=0),$ will print out to a local file called $$output$.$txt$,$ the centrality measures for all the vertices. The processor will also print five nodes with the top centrality values $($if there are more than five nodes with the centrality values, then print any five$)$ and also the average of the centrality values of all nodes on screen.

$$ Program design: You may use any APSPs algorithm to calculate the shortest paths required in centrality calculation. The key aspect of the project is to come up with a good parallel design. Points will be given for efficient design.

$$ Performance study: Tabulate the running times of your implementation with varying number of processors $=2,4,8,16,......$ perform your study using your chosen social networks. Prepare plots showing the trends in the run time. Answer questions, such as

o what is the parallel speedup for your implementation? Plot the speedup with P$=2,4,8,16...$

o What is the cost of the implementation? Plot the cost with various values of P$.$