page_rank  R Documentation 
Calculates the Google PageRank for the specified vertices.
page_rank(
graph,
algo = c("prpack", "arpack"),
vids = V(graph),
directed = TRUE,
damping = 0.85,
personalized = NULL,
weights = NULL,
options = NULL
)
graph 
The graph object. 
algo 
Character scalar, which implementation to use to carry out the
calculation. The default is 
vids 
The vertices of interest. 
directed 
Logical, if true directed paths will be considered for directed graphs. It is ignored for undirected graphs. 
damping 
The damping factor (‘d’ in the original paper). 
personalized 
Optional vector giving a probability distribution to calculate personalized PageRank. For personalized PageRank, the probability of jumping to a node when abandoning the random walk is not uniform, but it is given by this vector. The vector should contains an entry for each vertex and it will be rescaled to sum up to one. 
weights 
A numerical vector or 
options 
A named list, to override some ARPACK options. See

For the explanation of the PageRank algorithm, see the following webpage: http://infolab.stanford.edu/~backrub/google.html, or the following reference:
Sergey Brin and Larry Page: The Anatomy of a LargeScale Hypertextual Web Search Engine. Proceedings of the 7th WorldWide Web Conference, Brisbane, Australia, April 1998.
The page_rank()
function can use either the PRPACK library or ARPACK
(see arpack()
) to perform the calculation.
Please note that the PageRank of a given vertex depends on the PageRank of all other vertices, so even if you want to calculate the PageRank for only some of the vertices, all of them must be calculated. Requesting the PageRank for only some of the vertices does not result in any performance increase at all.
A named list with entries:
vector 
A numeric vector with the PageRank scores. 
value 
When using the ARPACK method, the eigenvalue corresponding to the eigenvector with the PageRank scores is returned here. It is expected to be exactly one, and can be used to check that ARPACK has successfully converged to the expected eingevector. When using the PRPACK method, it is always set to 1.0. 
options 
Some information
about the underlying ARPACK calculation. See 
Tamas Nepusz ntamas@gmail.com and Gabor Csardi csardi.gabor@gmail.com
Sergey Brin and Larry Page: The Anatomy of a LargeScale Hypertextual Web Search Engine. Proceedings of the 7th WorldWide Web Conference, Brisbane, Australia, April 1998.
Other centrality scores: closeness()
,
betweenness()
, degree()
Centrality measures
alpha_centrality()
,
betweenness()
,
closeness()
,
diversity()
,
eigen_centrality()
,
harmonic_centrality()
,
hub_score()
,
power_centrality()
,
spectrum()
,
strength()
,
subgraph_centrality()
g < sample_gnp(20, 5 / 20, directed = TRUE)
page_rank(g)$vector
g2 < make_star(10)
page_rank(g2)$vector
# Personalized PageRank
g3 < make_ring(10)
page_rank(g3)$vector
reset < seq(vcount(g3))
page_rank(g3, personalized = reset)$vector
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