PolyhedronData ["Archimedean"]

PolyhedronData ["Johnson"]

PolyhedronData["GreatRhombicosidodecahedron"]

PolyhedronData["GreatRhombicosidodecahedronGraph","Graph"]

GraphData["GreatRhombicosidodecahedralGraph"]

GraphData["GreatRhombicosidodecahedralGraph","LaplacianMatrix"]

GraphData["TruncatedDodecahedralGraph"]

GraphData["TruncatedIcosahedralGraph"]

GraphData["IcosidodecahedralGraph"]

GraphData["IcosidodecahedralGraph","IncidenceMatrix"]

MatrixForm[%]

G= MatrixForm[DirectedGraph[GraphData["IcosidodecahedralGraph","IncidenceMatrix"],"Random"]]

DirectedGraph[GraphData["IcosidodecahedralGraph","IncidenceMatrix"],"Random"]

DirectedGraph[GraphData["IcosidodecahedralGraph"], "Random"]

DirectedGraph["IcosidodecahedralGraph"]

Ga = DirectedGraph[GraphData["GreatRhombicosidodecahedralGraph"], "Random"]

Aa = IncidenceMatrix[Ga]

MatrixForm[%]

A = Drop[Aa,{1,1}]

MatrixForm[A]

K=A.Transpose[A]

MatrixForm[K]

{lu,p,c}=LUDecomposition[K];

det=Tr[lu,Times]

V=det*Inverse[K];

MatrixForm[V]

W=Apply[GCD,V,{1}]

Y=MatrixForm[V/W]

F=Transpose[A].V.A;

MatrixForm[F]

R=Apply[GCD,F,{1}]

B=MatrixForm[F/R]

W= {381293926,84446473,-69288361,5002466,-1174039,3828427,-46918172,-15787066,31131106,-2181164,2529052,347888,69288361,84446473,3436417,-1566049,-22370189,1255253,-5665718,-10615502,-16281220,-6378370,712652,77234396,7212077,-3572716,-4746755,3455786,2085190,1370596,1902458,-5358244,-25564,15812630,-2181164,-347888,-7212077,-77234396,-3125621,-1559572,-29582266,4380874,-1428586,9186916,7806956,-57932188,-19302208,-2610266,-962450,3638518,-5723708,1736060,-10727219,-10701655,1255253,-3436417,19302208,-1050694,-18855047,3125621,15812630,16281220,-468590,2085190,-1370596,3455786,14555816,-9186916,5368900,-6078724,5723708,355016,15787066,-25564,3638518,5723708,5368900,-9186916,1430512,-7509236,-22370189,-46918172,2092367,-1736060,-468590,-30662516,-3224828,3572716,18855047,2573827,-4672325,5384977,-29582266,-6839122,-16281220,3572716,6186530,4815934,-5003228,355016,-31131106,-1902458,25293616,5003228,-6186530,10094690,-4815934,-907774,-10727219,2166797,10094690,1430512,-30662516,-5358244,13275482,-10701655,7890505,5723708,-907774,6078724,-4752448,4778012,-25564,-2423270,-4159330,-1736060,-5384977,13275482,-7890505,1174039,-5002466,-3828427,-5121556,9874004,-2934974,5358244,-4672325,-712652,-4746755,3572716,2934974,3647626,-712652,2423270,5358244,-4159330,-7806956,1736060,712652,-4408904,3647626,6839122,2166797,-2092367,19327772,2698510,2573827,1566049,4778012,25564,-4752448,4151464,-3749204,402260,10615502,-16281220,5665718,1050694,-1559572,-2610266,9186916,-4408904,3749204,-402260,-1428586,-2698510,5121556,-4955984,-6378370,-962450}

Graph[Ga,EdgeWeight->W]

Graph[Wg,EdgeLabels-> "EdgeWeight"]

Cm[[1]]