This paper develops a generalization of the PageRank model of page centralities in the global webgraph of hyperlinks. The webgraph of adjacencies is generalized to a valued directed graph, and the scalar dampening coefficient for walks through the graph is relaxed to allow for heterogeneous values. A visitation count approach may be employed to apply the more general model, based on the number of visits to a page and the page's proportionate allocations of these visits to other nodes of the webgraph.