Presented at the First openCypher Implementers Meeting in Walldorf, Germany, February 2017 @ http://www.opencypher.org/blog/2017/03/31/first-ocim-blog/

1. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. |
Graph pattern matching semantics
First openCypher Implementers Meeting
Oskar van Rest
Oracle
February 8, 2017

2. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. |
Safe Harbor Statement
The following is intended to outline our general product direction. It is intended for
information purposes only, and may not be incorporated into any contract. It is not a
commitment to deliver any material, code, or functionality, and should not be relied upon
in making purchasing decisions. The development, release, and timing of any features or
functionality described for Oracle’s products remains at the sole discretion of Oracle.
2

3. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. |
Graph pattern matching semantics
Isomorphism
• Two query vertices may
not map to the same data
vertex
– Semantic for multi-graphs is
undefined
Cyphermorphism
• Two query edges may not
map to the same data
edge
Homomorphism
• No restriction
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less restrictive (more powerful)
easier to get started with
For most queries, this works very well: users
who are not aware of the semantic still get the
desired result.

4. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. |
:Person
name = ‘John’
When does the semantic fails?
Isomorphism Cyphermorphism
4
MATCH (n:Function) -[:calls]-> (m)
WHERE n.name = ‘factorial’
RETURN m.name
:Function
name = ‘factorial’
100
:Function
name = ‘factorial_helper’
200
1 :calls
codeGraph0
:calls
m.name
‘factorial’
‘factorialHelper’
Result with isomorphism
m.name
‘factorialHelper’
Result with homomorphism
Query: which functions are
called by function ‘factorial’
:Person
name = ‘Ann’
200
100
familyTree
MATCH
(n:Person) -[:has_parent]-> () –[:has_parent]- (grandparent)
(m:Person) -[:has_parent]-> () –[:has_parent]- (grandparent)
WHERE n <> m
RETURN grandparent.name Query: “find common
grandparents”
300 400
:has_parent
:has_parent
0
:has_parent
1
2
:Person
name = ‘Klara’
:Person
name = ‘Amber’
grandparent.name
‘Amber’
Result with cyphermorphism
grandparent.name
Result with homomorphism

5. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. |
Pros and cons of the different semantics
• They all have the same worst-case time complexity: O(nk) (n = num. data vertices, k =
num. query vertices)
– However, if we apply iso/cypher-morphism to recursive path queries, things blow up
• Isomorphism & cyphermorphism have limitations (see previous slide)
• Homomorphism may return more matches than expected and requires
additional non-equality constraints
• Isomorphism & cyphermorphism don’t translate as well to/from SQL
5

6. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. |
Safe Harbor Statement
The preceding is intended to outline our general product direction. It is intended for
information purposes only, and may not be incorporated into any contract. It is not a
commitment to deliver any material, code, or functionality, and should not be relied upon
in making purchasing decisions. The development, release, and timing of any features or
functionality described for Oracle’s products remains at the sole discretion of Oracle.
6