---
title: "Finding the paths in a directed cyclic graph"
url: "https://docs.yugabyte.com/stable/api/ysql/the-sql-language/with-clause/traversing-general-graphs/directed-cyclic-graph/"
---

# Finding the paths in a directed cyclic graph

This section shows how to use a recursive CTE to traverse a directed cyclic graph.

Before trying the code in this section, make sure that you have created the *"edges"* table (see [`cr-edges.sql`](/stable/api/ysql/the-sql-language/with-clause/traversing-general-graphs/graph-representation/#cr-edges-sql "cr-edges.sql")) and installed all the code shown in the section [Common code for traversing all kinds of graph](/stable/api/ysql/the-sql-language/with-clause/traversing-general-graphs/common-code/ "Common code for traversing all kinds of graph").

First, define a suitable constraint on the *"edges*" table for representing a directed cyclic graph and populate the table with the data that represents the graph shown in the [Directed cyclic graph](/stable/api/ysql/the-sql-language/with-clause/traversing-general-graphs/#directed-cyclic-graph "Directed cyclic graph") section.

```plpgsql
delete from edges;
alter table edges drop constraint if exists edges_chk cascade;
alter table edges add constraint edges_chk check(node_1 <> node_2);

insert into edges(node_1, node_2) values
  ('n2', 'n1'),
  ('n2', 'n4'),
  ('n4', 'n5'),
  ('n4', 'n6'),
  ('n6', 'n4'),
  ('n5', 'n6'),
  ('n5', 'n3'),
  ('n3', 'n2');
```

Now reinstate the implementation of *"find\_paths()"* shown at [cr-find-paths-with-nocycle-check.sql](/stable/api/ysql/the-sql-language/with-clause/traversing-general-graphs/undirected-cyclic-graph/#cr-find-paths-with-nocycle-check-sql "cr-find-paths-with-nocycle-check.sql").

Find all the paths from *"n2"* and create the filtered subset of shortest paths to the distinct terminal nodes:

```plpgsql
call find_paths(start_node => 'n2');
call restrict_to_shortest_paths('raw_paths', 'shortest_paths');
```

Look at the *"raw\_paths"*:

```plpgsql
\t on
select t from list_paths('raw_paths');
\t off
```

This is the result:

```
 path #   cardinality   path
 ------   -----------   ----
      1             2   n2 > n1
      2             2   n2 > n4
      3             3   n2 > n4 > n5
      4             3   n2 > n4 > n6
      5             4   n2 > n4 > n5 > n3
      6             4   n2 > n4 > n5 > n6
```

Look at the "*filtered\_paths"*:

```plpgsql
\t on
select t from list_paths('shortest_paths');
\t off
```

This is the result:

```
 path #   cardinality   path
 ------   -----------   ----
      1             2   n2 > n1
      2             2   n2 > n4
      3             3   n2 > n4 > n5
      4             3   n2 > n4 > n6
      5             4   n2 > n4 > n5 > n3
```