Calculating PageRank with Apache Age

Graph databases provide a robust way to handle complex data relationships. Apache Age, an extension of PostgreSQL, is a compelling solution that offers the strengths of a relational database with the additional power of a graph database.

In this article, we'll explore how to implement a popular graph algorithm, PageRank, in Apache Age. Originally developed by the founders of Google, the PageRank algorithm assigns a numerical weight to each node in a graph to estimate its relative importance within the set.

Understanding PageRank

PageRank works on the premise that significant nodes are likely to receive more links from other nodes. In the world of web page ranking, for example, a webpage is considered important if it has many pages linking to it. Moreover, pages with their high rank and more links contribute more to the rank of the page to which they link.

PageRank is iterative and recursive in nature - each node's rank is dependent on the ranks of the nodes linking to it, and those ranks are, in turn, dependent on the ranks of nodes linking to them, and so forth.

Implementing PageRank in Apache Age

Apache Age doesn't come with a built-in function for calculating PageRank. However, thanks to the underlying PostgreSQL functionality, you can write a custom function to calculate PageRank. Here is a simplified version of how you can approach this.

CREATE OR REPLACE FUNCTION pagerank(ITERATIONS integer) RETURNS TABLE (node_id integer, rank double precision) AS
$$
DECLARE
  i integer := 0;
BEGIN
  -- Initialize rank of all nodes to 1
  CREATE TEMPORARY TABLE temp_pagerank AS
    SELECT id AS node_id, 1.0 AS rank
    FROM node_table;

  -- Iterate ITERATIONS times
  WHILE i < ITERATIONS LOOP
    -- Update the rank based on the sum of the rank of the incoming nodes, divided by their out-degree.
    WITH new_ranks AS (
      SELECT e.target_id AS node_id, SUM(temp_pagerank.rank / out_degrees.out_degree) AS rank
      FROM edge_table AS e
      JOIN temp_pagerank ON temp_pagerank.node_id = e.source_id
      JOIN (
        SELECT source_id, count(*) AS out_degree
        FROM edge_table
        GROUP BY source_id
      ) AS out_degrees ON out_degrees.source_id = e.source_id
      GROUP BY e.target_id
    )
    UPDATE temp_pagerank
    SET rank = 0.15 + 0.85 * new_ranks.rank
    FROM new_ranks
    WHERE new_ranks.node_id = temp_pagerank.node_id;

    i := i + 1;
  END LOOP;

  RETURN QUERY SELECT * FROM temp_pagerank;
END;
$$
LANGUAGE plpgsql;

In this script, node_table represents the table with your nodes, and edge_table represents the table with your edges, with source_id and target_id as the source and target nodes of each edge, respectively. It also assumes that the graph is fully connected, which might not be the case in your data.

Executing the Function

Once you have defined the function, you can call it with the number of iterations as a parameter, like this:

SELECT * FROM pagerank(20);

This will return the rank for each node after 20 iterations.

Conclusion

While Apache Age might not natively support PageRank, the extensible nature

of PostgreSQL allows you to create a custom implementation of the PageRank algorithm. As the project evolves, it's likely that more graph algorithms will be incorporated directly into Apache Age. Until then, leveraging the inherent capabilities of PostgreSQL can fill the gap for advanced graph operations such as PageRank. Remember to be mindful of the computational complexity and structure of your graph when implementing such algorithms.