Weighted Page Rank Algorithm in Neo4j using Cypher

weighted-page-rank.cypher

/* we have to go through all nodes */
MATCH (node:Page)
WITH
COLLECT(distinct node) AS pages
UNWIND pages as dest
  /* let's find all source citations for a given node */
  MATCH (source:Page)-[:NEXT]->(dest)
  WITH
    COLLECT(DISTINCT source) AS sources,
    dest AS dest
    UNWIND sources AS src
      /* we have to know how many relationships the source node has */
      MATCH (src)-[r:NEXT]->(dest)
      WITH src, dest, sum(r.weight) AS prob
      MATCH (src)-[r:NEXT]->()
      WITH
      /* The source citation will pass a portion of its pagerank as juice */
        src.pagerank * (prob/ sum(r.weight)) AS juice,
        dest AS dest
      /* now we have all information to update the destination node with the new pagerank */
      WITH
        sum(juice) AS p,
        dest AS dest
      /* Using damping factor d = 0.85 */
      set dest.pagerank = 0.15 + 0.85 * p;