Page rank centrality is a centrality measure for vertices in a graph, originally motivated by assigning importance to web pages from the links among them,
and was an ingredient in the early Google search engine (Brin and Page 1998). With
damping parameter 
and initial centralities 
, it is a normalized centrality vector obtained by iteratively
distributing score along outgoing edges and mixing in the initial centralities.
Although originally developed for ranking web pages, PageRank has also been applied to other networks, including bibliometric, social, information, biological, and transportation networks (Gleich 2015), for example to find structurally important species in food chains or proteins in metabolic cellular networks.
In the original web-page formulation, the total page rank over all pages was taken to be the number of pages, while probability-normalized formulations instead take the entries of the page rank vector to sum to 1.
Page rank centrality is implemented in the Wolfram Language as PageRankCentrality[g, alpha] and PageRankCentrality[g, alpha, beta], and precomputed symbolic values for many named graphs can be obtained using GraphData[graph, "PageRankCentralities"].
