PageRank Centrality

PageRank (Brin and Page 1998) is the stationary distribution of a random walk that follows an out-edge with probability $d$, choosing edges in proportion to their weights, and otherwise jumps to a node drawn from the reset distribution $p$: $$PR = (1 - d)\,p + d\,P^{T} PR,$$ where $P$ is the row-normalized weight matrix and $d$ is damping.

Usage

centrality_pagerank(x, damping = 0.85, personalized = NULL, ...)

Arguments

x: Network input accepted by centrality.
damping: Probability $d$ of following an edge (default 0.85).
personalized: Reset distribution $p$, a non-negative numeric vector with one entry per node, named by node or in input node order. The default NULL gives the uniform distribution.
...: Further arguments to centrality.

Value

A named numeric vector with one score per node, in input node order.

Details

weighted = FALSE gives every edge weight one. A node without out-edges passes its score to the reset distribution. The scores sum to one and equal igraph::page_rank(). The vector personalized is rescaled to sum to one. A named vector is matched to the node names, and its names must be the node names, each used once; an unnamed vector is matched by position. A negative weight raises a cograph_negative_weights error, an invalid personalized a cograph_bad_input error, and a damping outside $[0, 1]$ a cograph_bad_parameter error.

References

Brin, S., & Page, L. (1998). The anatomy of a large-scale hypertextual Web search engine. Computer Networks and ISDN Systems, 30(1-7), 107-117. doi:10.1016/S0169-7552(98)00110-X .

Examples

centrality_pagerank(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#> 0.11846147 0.03640953 0.18376724 0.12356096 0.12513119 0.06803638 0.03760071 
#>   Evaluate     Create      Share 
#> 0.07386400 0.13821279 0.09495573