page.rank {igraph} | R Documentation |
Calculates the Google PageRank for the specified vertices.
page.rank (graph, vids = V(graph), directed = TRUE, damping = 0.85, weights = NULL, options = igraph.arpack.default) page.rank.old (graph, vids = V(graph), directed = TRUE, niter = 1000, eps = 0.001, damping = 0.85, old = FALSE)
graph |
The graph object. |
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). |
weights |
A numerical vector or |
options |
A named list, to override some ARPACK options. See
|
niter |
The maximum number of iterations to perform. |
eps |
The algorithm will consider the calculation as complete if the difference of PageRank values between iterations change less than this value for every node. |
old |
A logical scalar, whether the old style (pre igraph 0.5) normalization to use. See details below. |
For the explanation of the PageRank algorithm, see the following webpage: http://www-db.stanford.edu/~backrub/google.html, or the following reference:
Sergey Brin and Larry Page: The Anatomy of a Large-Scale Hypertextual Web Search Engine. Proceedings of the 7th World-Wide Web Conference, Brisbane, Australia, April 1998.
igraph 0.5 (and later) contains two PageRank calculation
implementations. The page.rank
function uses ARPACK to perform
the calculation, see also arpack
.
The page.rank.old
function performs a simple power method, this
is the implementation that was available under the name
page.rank
in pre 0.5 igraph versions. Note that
page.rank.old
has an argument called old
. If this
argument is FALSE
(the default), then the proper PageRank
algorithm is used, i.e. (1-d)/n is added to the weighted
PageRank of vertices to calculate the next iteration. If this
argument is TRUE
then (1-d) is added, just like in the
PageRank paper; d is the damping factor, and n is the
total number of vertices.
A further difference is that the old implementation does not
renormalize the page rank vector after each iteration.
Note that the old=FALSE
method is not stable,
is does not necessarily converge to a fixed point. It should be
avoided for new code, it is only included for compatibility with old
igraph versions.
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.
Since the calculation is an iterative process, the algorithm is stopped after a given count of iterations or if the PageRank value differences between iterations are less than a predefined value.
For page.rank
a named list with entries:
vector |
A numeric vector with the PageRank scores. |
value |
The eigenvalue corresponding to the eigenvector with the page rank scores. It should be always exactly one. |
options |
Some information about the underlying ARPACK
calculation. See |
For page.rank.old
a numeric vector of Page Rank scores.
Tamas Nepusz ntamas@rmki.kfki.hu and Gabor Csardi csardi@rmki.kfki.hu
Sergey Brin and Larry Page: The Anatomy of a Large-Scale Hypertextual Web Search Engine. Proceedings of the 7th World-Wide Web Conference, Brisbane, Australia, April 1998.
Other centrality scores: closeness
,
betweenness
, degree
g <- random.graph.game(20, 5/20, directed=TRUE) page.rank(g)$vector g2 <- graph.star(10) page.rank(g2)$vector