In[]:=
G=Graph[{1->2,2->3,2->4,3->4},EdgeWeight{0.5,0.6,0.4,0.5}]​​A=WeightedAdjacencyMatrix[G]​​Grid[{​​{"A",MatrixForm[A],GraphPlot[A,EdgeLabels->Automatic]},​​{"A.A",MatrixForm[A.A],GraphPlot[A.A,EdgeLabels->Automatic]},​​{"A.A.A",MatrixForm[A.A.A],GraphPlot[A.A.A,EdgeLabels->Automatic]},​​{"A+A.A+A.A.A",MatrixForm[A+A.A+A.A.A],GraphPlot[A+A.A+A.A.A,EdgeLabels->Automatic]}​​},Frame->All]
Out[]=
Out[]=
SparseArray
Specified elements: 4
Dimensions: {4,4}

Out[]=
A
0
0.5
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0.6
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0.5
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A.A
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A.A.A
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0.15
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A+A.A+A.A.A
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0.35
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