Given a (weighted) adjacency matrix, compute the PageRank: the the stationary distribution of a random walk around the graph.
PageRank(C, alpha = 0.85, sort = FALSE)
| C | a square matrix |
|---|---|
| alpha | a damping factor |
| sort | logical. Reorder the indices in descending order of PageRank |
A PageRank vector, scaled to sum to one
PageRank is an eigenvector centrality metric, equivalent to Pinski & Narin's influence weight (1976)
with the addition of a damping factor alpha, which simulates a random surfer traversing the graph and
teleporting at any time with probability 1 - alpha. The effect of the damping factor is to smooth out
any disconnected components or transient portions of the network.
In bibliometrics, PageRank has also been implemented as the Eigenfactor Metric and as the SCImago Journal Rank.
By default, C[i,j] refers to the directed edge that points from column j to row i.
Use t(C) if you want edges directed from rows to columns instead.
Pinski, G., & Narin, F. (1976). Citation influence for journal aggregates of scientific publications: Theory, with application to the literature of physics. Information Processing & Management, 12(5), 297--312.
Page, L., Brin, S., Motwani, R., & Winograd, T. (1999). The PageRank citation ranking: bringing order to the web. Technical Report, Stanford InfoLab.
Other network centrality estimators: BTscores,
BradleyTerry, ILSR,
Scroogefactor
PageRank(citations)#> AmS AISM AoS ANZS Bern BioJ #> 0.012202138 0.010862596 0.098915149 0.006697535 0.015483828 0.012464668 #> Bcs Bka Biost CJS CSSC CSTM #> 0.059136945 0.058378620 0.023982870 0.012621280 0.007618752 0.014087489 #> CmpSt CSDA EES Envr ISR JABES #> 0.006069933 0.039376887 0.007432336 0.009385664 0.008349565 0.006919707 #> JASA JAS JBS JCGS JMA JNS #> 0.110303393 0.006908512 0.008526762 0.022145121 0.027459149 0.009329186 #> JRSS-A JRSS-B JRSS-C JSCS JSPI JSS #> 0.012862422 0.067875638 0.011081492 0.008798648 0.037841892 0.009230503 #> JTSA LDA Mtka SJS StataJ StCmp #> 0.008850493 0.009731145 0.007994149 0.019257984 0.010430958 0.012695927 #> Stats StMed SMMR StMod StNee StPap #> 0.006542398 0.061516023 0.008532377 0.006185163 0.005717473 0.005254096 #> SPL StSci StSin Tech Test #> 0.024401487 0.020397719 0.027139599 0.013314648 0.009689682# Scroogefactor, an estimator for the Bradley-Terry model PageRank(citations)/colSums(citations)#> AmS AISM AoS ANZS Bern BioJ #> 7.395235e-05 6.664169e-05 1.231820e-04 6.765187e-05 7.741914e-05 2.960729e-05 #> Bcs Bka Biost CJS CSSC CSTM #> 7.457370e-05 1.172261e-04 6.680465e-05 5.897795e-05 1.822668e-05 2.194313e-05 #> CmpSt CSDA EES Envr ISR JABES #> 4.895107e-05 2.297368e-05 5.546519e-05 5.272845e-05 1.043696e-04 5.766422e-05 #> JASA JAS JBS JCGS JMA JNS #> 1.107464e-04 1.775967e-05 2.292140e-05 7.260695e-05 2.597838e-05 3.205906e-05 #> JRSS-A JRSS-B JRSS-C JSCS JSPI JSS #> 1.004877e-04 2.620681e-04 5.083253e-05 2.802117e-05 2.832477e-05 3.205036e-05 #> JTSA LDA Mtka SJS StataJ StCmp #> 8.349522e-05 5.094840e-05 4.844939e-05 7.860402e-05 9.070398e-05 4.755029e-05 #> Stats StMed SMMR StMod StNee StPap #> 4.450611e-05 3.676989e-05 3.440475e-05 5.425582e-05 7.425289e-05 2.871090e-05 #> SPL StSci StSin Tech Test #> 3.714077e-05 4.879837e-05 4.441833e-05 7.197107e-05 3.166563e-05