Centrality in Citation Networks
Centrality in Citation Networks
The Wolfram Language provides several centrality measures for citation networks. The centrality measures can easily be compared by means of cumulative distribution plots.
g = [image];
centralities = {{"HITS authority", HITSCentrality[#][[1]]&}, {"HITS hub", HITSCentrality[#][[2]]&}, {"Eigenvector", EigenvectorCentrality}, {"Katz α=0.1", KatzCentrality[#, 0.1]&}, {"Page-rank α=0.99", PageRankCentrality[#, 0.99]&}};
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 -> {-0.001Length[scores], Length[scores]}, ImageSize -> {150, Automatic}, PlotLabel -> Style[title, 12, FontFamily -> "Verdana"]]];
GraphicsGrid[(| | | |
| ------------- | ------------- | ------------- |
| g | SpanFromLeft | plotScores[1] |
| SpanFromAbove | SpanFromBoth | plotScores[2] |
| plotScores[3] | plotScores[4] | plotScores[5] |), Spacings -> {5, 15}]