PageRankCentrality gives solution to eigenproblem c=α A (A^T)D c+β

g=RandomGraph[{100,1000}];
PageRankCentrality[g,0.5];
HighlightGraph[g,VertexList[g],VertexSize->Thread[VertexList[g]->Rescale[%]]]

g=ExampleData[{"NetworkGraph","SimpleFoodWeb"}]
c=PageRankCentrality[ReverseGraph[g],0.85];
Pick[VertexList[g],c,Max[c]]

IncidenceMatrix[g] // MatrixForm

VertexList[g]

g=ExampleData[{"NetworkGraph","AmericanCollegeFootball"}]

VertexList[g]

c=PageRankCentrality[ReverseGraph[g],0.85];
Pick[VertexList[g],c,Max[c]]

g=ExampleData[{"NetworkGraph","PowerGrid"}]

c=PageRankCentrality[ReverseGraph[g],0.85];
Pick[VertexList[g],c,Max[c]]

ExampleData["NetworkGraph"]