This function computes the average of the shortest paths between each pair of vertices. Average path length is based on "reachable target vertices", so it ignores infinite-length paths between vertices that are not connected. This means the function will average the path lengths in each connected component. If the user requires the average path length of a particular component, the weakly_connected_components function may be used to isolate the relevant vertices.

Note

This function assumes a valid output from a prior APSP run - both the APSP table and the associated output summary table. APSP is a computationally expensive algorithm because it finds the shortest path between all nodes in the graph. The worst case run-time for this implementation is O(V^2 * E) where V is the number of vertices and E is the number of edges. In practice, run-time will be generally be much less than this, depending on the graph.

Average Path Length

graph_avg_path_length( apsp_table,
                       output_table
                     )

Arguments

apsp_table

TEXT. Name of the output table generated by a prior run of all pairs shortest path (APSP).

out_table

TEXT. Name of the table to store the average path length. It contains a row for every group, and the average path value.

Examples

1. Create vertex and edge tables to represent the graph:

   DROP TABLE IF EXISTS vertex, edge;
   CREATE TABLE vertex(
           id INTEGER,
           name TEXT
           );
   CREATE TABLE edge(
           src_id INTEGER,
           dest_id INTEGER,
           edge_weight FLOAT8
           );
   INSERT INTO vertex VALUES
   (0, 'A'),
   (1, 'B'),
   (2, 'C'),
   (3, 'D'),
   (4, 'E'),
   (5, 'F'),
   (6, 'G'),
   (7, 'H');
   INSERT INTO edge VALUES
   (0, 1, 1.0),
   (0, 2, 1.0),
   (0, 4, 10.0),
   (1, 2, 2.0),
   (1, 3, 10.0),
   (2, 3, 1.0),
   (2, 5, 1.0),
   (2, 6, 3.0),
   (3, 0, 1.0),
   (4, 0, -2.0),
   (5, 6, 1.0),
   (6, 7, 1.0);
   

2. Calculate the all-pair shortest paths:

   DROP TABLE IF EXISTS out_apsp, out_apsp_summary;
   SELECT madlib.graph_apsp('vertex',      -- Vertex table
                            'id',          -- Vertix id column (NULL means use default naming)
                            'edge',        -- Edge table
                            'src=src_id, dest=dest_id, weight=edge_weight',
                                           -- Edge arguments (NULL means use default naming)
                            'out_apsp');        -- Output table of shortest paths
   

3. Compute the average path length measure:

   DROP TABLE IF EXISTS out_avg_path_length;
   SELECT madlib.graph_avg_path_length('out_apsp', 'out_avg_path_length');
   SELECT * FROM out_avg_path_length;
   

    avg_path_length
   ------------------
    2.973684210526316
   (1 row)
   

4. Create a graph with 2 groups and find APSP for each group:

   DROP TABLE IF EXISTS edge_gr;
   CREATE TABLE edge_gr AS
   (
     SELECT *, 0 AS grp FROM edge
     UNION
     SELECT *, 1 AS grp FROM edge WHERE src_id < 6 AND dest_id < 6
   );
   INSERT INTO edge_gr VALUES
   (4,5,-20,1);
   

5. Find APSP for all groups:

   DROP TABLE IF EXISTS out_gr, out_gr_summary;
   SELECT madlib.graph_apsp(
                            'vertex',      -- Vertex table
                            NULL,          -- Vertex id column (NULL means use default naming)
                            'edge_gr',     -- Edge table
                            'src=src_id, dest=dest_id, weight=edge_weight',
                            'out_gr',      -- Output table of shortest paths
                            'grp'          -- Grouping columns
   );
   

6. Find the average path length in every group

   DROP TABLE IF EXISTS out_gr_path;
   SELECT madlib.graph_avg_path_length('out_gr', 'out_gr_path');
   SELECT * FROM out_gr_path ORDER BY grp;
   

    grp |  avg_path_length
   ----—+-------------------—
      0 |  2.973684210526316
      1 |               0.56
   (2 rows)