just fyi, PageRank and BM25 address orthogonal problems of reputation/popularity (PageRank) and query/semantic matching (BM25). Saying you're using bm25 instead of PageRank makes no sense.
both are similar in the sense that they can be used to sort a series of sites/documents by relevance. PageRank makes the assumption that sites with better in/out links are more relevant, while BM25 makes the assumption that documents with high keyword matching are more relevant. In this sense both solutions are similar.
