## 6.12. Pretty graphs

This section is showing how to create some of the named pretty graphs on Wikipedia.

### Star graph

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.

Result

id
1 row
Nodes created: 7
Relationships created: 6

0

Try this query live none create (center) foreach( x in range(1,6) | create (leaf), (center)-[:X]->(leaf) ) return id(center) as id;

### Wheel graph

This graph is created in a number of steps:

• Create a center node.
• Once per element in the range, create a leaf and connect it to the center.
• Connect neighboring leafs.
• Find the minimum and maximum leaf and connect these.
• Return the id of the center node.

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.

Result

id
1 row
Nodes created: 7
Relationships created: 12
Properties set: 6

0

Try this query live none 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

### Complete 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.

Result

Nodes created: 6
Relationships created: 15
Properties set: 6

(empty result)

Try this query live none 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);

### Friendship 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.

Result

id
1 row
Nodes created: 7
Relationships created: 9

0

Try this query live none 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