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8: Graph & Network Analysis
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Centrality in Citation Networks
Mathematica
8 provides several centrality measures for citation networks. The centrality measures can easily be compared by means of cumulative distribution plots.
In[1]:=
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In[2]:=
X
centralities = {{"HITS authority", HITSCentrality[#][[1]] &}, {"HITS hub", HITSCentrality[#][[2]] &}, {"Eigenvector", EigenvectorCentrality}, {"Katz \[Alpha]=0.1", KatzCentrality[#, 0.1] &}, {"Page-rank \[Alpha]=0.99", PageRankCentrality[#, 0.99] &}};
In[3]:=
X
plotScores[i_] := With[{title = centralities[[i, 1]], scores = centralities[[i, 2]][g]}, Plot[Count[scores, s_ /; s <= x], {x, -0.01*Max[scores], 1.01*Max[scores]}, Filling -> Axis, PlotStyle -> Directive[Thick, Orange], FillingStyle -> Hue[0.15, 0.5, 0.9], Axes -> {True, False}, Ticks -> {None, None}, AxesStyle -> LightGray, PlotRange -> {-0.001 Length[scores], Length[scores]}, ImageSize -> {150, Automatic}, PlotLabel -> Style[title, 12, FontFamily -> "Verdana"]]];
In[4]:=
X
GraphicsGrid[( { {g, SpanFromLeft, plotScores[1]}, {SpanFromAbove, SpanFromBoth, plotScores[2]}, {plotScores[3], plotScores[4], plotScores[5]} } ), Spacings -> {5, 15}]
Out[4]=