The following Maple code generating 5 nodes and 9 edges has been used in class for demonstration. You may use it as an archetype to produce your own code. You may also use Matlabs commands digraph and centrality or any other software packages that are at your disposal to answer the work.

restart;

with(GraphTheory);

G:=Graph([P1,P2,P3,P4,P5],{[P1,P2],[P2,P1],[P2,P3],[P2,P4],[P3,P4],[P3,P5],[P4,P5],[P5,P1],[P5,P4]});

DrawGraph(G);

AR:=Arrivals(G);

Authority:=map(numelems, AR);

A:= AdjacencyMatrix(G);

DP:=Departures(G); Hub:=map(numelems, DP);

n:=5;

Google:=A;

for i to n do

s:=numelems(DP[i]);

for j to n do

Google[i, j]:=A[i, j]/s;

end do;

end do;

Google;

with(LinearAlgebra);

B:=Transpose(Google);

Q:=Vector([1/5, 1/5, 1/5, 1/5, 1/5]);

for k to 10 do Q:=MatrixVectorMultiply(B, Q);

end do;

evalf(Q);

a)Calculate the associated 10 10 Google matrix G.

b) Use the power method to calculate the ultimate PageRank of each node. Note that PageRank is a probability vector, so its entries sum to 1.