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],PathGraph[Range[83,93]],CompleteGraph[41],PathGraph[Range[94,104]]];

Graph[CC,VertexLabels->"Name"]

DD=EdgeAdd[CC,{145\[UndirectedEdge]42,83\[UndirectedEdge]40,93\[UndirectedEdge]118,135\[UndirectedEdge]110}]

{Position[VertexDegree[DD],Max[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];

dim=Dimensions[MM][[1]];

maxeig=Max[N[Eigenvalues[MM]]];

firstvect=Chop[Normalize[NullSpace[MM-maxeig*IdentityMatrix[dim]][[1]]],10^(-4)]

result=Chop[Normalize[Nest[N[#.MM/(Norm[#.MM])]&,Table[1,{i,Range[dim]}],2000]],10^(-4)]

Position[firstvect,Max[firstvect]]

So we have that the 110th vertex is the most important 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[dim]}]

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

PageRank[0.3]

Module[{x=Table[1,{i,Range[dim]}].Inverse[IdentityMatrix[dim]-0.9*NN]},Position[x,Max[x]]]

Let us try the built-in function for PageRank:

Table[Module[{x=PageRankCentrality[DD,a]},Position[x,Max[x]][[1]][[1]]],{a,0,1,0.001}]

Results for a simpler graph:

G=Graph[{1\[UndirectedEdge]2,2\[UndirectedEdge]3,1\[UndirectedEdge]3,1\[UndirectedEdge]4},VertexLabels->"Name"]

adj = Normal@AdjacencyMatrix[G]

TraditionalForm[adj]

m=Max[N@Eigenvalues[adj]];

f=Chop[Normalize[NullSpace[adj-m*IdentityMatrix[4]][[1]]],10^(-4)]

r=Chop[Normalize[Nest[N[#.adj/(Norm[#.adj]^2)]&,Table[1,{i,Range[4]}],2000]],10^(-4)]

Hence we have that vertex number 1 is the most important

mark=adj/Map[Plus@@#&,adj];

FS[alpha_,vect_]:=alpha*vect.mark+Table[1-alpha,{i,Range[4]}]

PR[alpha_]:=Module[{x=Nest[FS[alpha,#]&,Table[1,{i,Range[4]}],2000]},Position[x,Max[x]]]

Table[PR[x],{x,0,0.99,0.0001}]