The graph is created by first creating a center node, and then once per element in the range, creates a leaf node and connects it to the center.

Query. 

CREATE (center)
FOREACH (x IN range(1,6)| CREATE (leaf),(center)-[:X]->(leaf))
RETURN id(center) AS id;

The query returns the id of the center node.

Figure 5.11. Graph

This graph is created in a number of steps:

Query. 

CREATE (center)
FOREACH (x IN range(1,6)| CREATE (leaf { count:x }),(center)-[:X]->(leaf))
WITH center
MATCH (large_leaf)<--(center)-->(small_leaf)
WHERE large_leaf.count = small_leaf.count + 1
CREATE (small_leaf)-[:X]->(large_leaf)
WITH center, min(small_leaf.count) AS min, max(large_leaf.count) AS max
MATCH (first_leaf)<--(center)-->(last_leaf)
WHERE first_leaf.count = min AND last_leaf.count = max
CREATE (last_leaf)-[:X]->(first_leaf)
RETURN id(center) AS id

The query returns the id of the center node.

Figure 5.12. Graph

To create this graph, we first create 6 nodes and label them with the Leaf label. We then match all the unique pairs of nodes, and create a relationship between them.

Query. 

FOREACH (x IN range(1,6)| CREATE (leaf:Leaf { count : x }))
WITH *
MATCH (leaf1:Leaf),(leaf2:Leaf)
WHERE id(leaf1)< id(leaf2)
CREATE (leaf1)-[:X]->(leaf2);

Nothing is returned by this query.

Figure 5.13. Graph

This query first creates a center node, and then once per element in the range, creates a cycle graph and connects it to the center

Query. 

CREATE (center)
FOREACH (x IN range(1,3)| CREATE (leaf1),(leaf2),(center)-[:X]->(leaf1),(center)-[:X]->(leaf2),
  (leaf1)-[:X]->(leaf2))
RETURN ID(center) AS id

The id of the center node is returned by the query.

Figure 5.14. Graph