N[3*100^(-3/4)]

First guess at importance measure: indegree;
Second guess: iterated indegree; (1,1,1,1...1)*A “many times”

A=GraphDisjointUnion@@Join[Table[CompleteGraph[10],{i,1,4}],{Graph[{41},{}]}]

B=EdgeAdd[A,Table[41\[UndirectedEdge]i,{i,1,40}]]

CC=GraphDisjointUnion[B,StarGraph[41]];

Graph[CC,VertexLabels->"Name"]

DD=EdgeAdd[CC,40\[UndirectedEdge]42]

Position[VertexDegree[DD],Max[VertexDegree[DD]]]

Hence we have that the vertex with the total indegree is number 42, with degree 41.

MM=Normal@AdjacencyMatrix[DD];

eigsys=N[Eigensystem[MM]];

firstvect=Normalize[eigsys[[2]][[1]]]

result=Normalize[Nest[N[#.MM/(Norm[#.MM]^2)]&,Table[1,{i,Range[82]}],2000]]

firstvect==result

Position[firstvect,Max[firstvect]]

So we have that the 41st vertex is more important than the 42nd by this method.

NN=MM/Map[Plus@@#&,MM];

NN is the Markov transition matrix belonging to MM.
alpha \in (0,1); x_{t+1}:=w/ prob. alpha, do previous, w/ prob. 1-alpha, give back (1,1,1,1,1...1)

Func[alpha_,vect_]:=alpha*vect.NN+Table[1-alpha,{i,Range[82]}]

PageRank[alpha_]:=Module[{x=Nest[Func[alpha,#]&,Table[1,{i,Range[82]}],2000]},Position[x,Max[x]]]

PageRank[1]