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Cypher Algebra
From ChatGPT (unedited):
Prompt:
In the relational database world, there's both relational calculus and relational algebra. The former is used as a way of expressing declaratively what the intent is, whereas the latter is more relevant to the kinds of operations implementers need to think about when implementing SQL. I'm curious about a similar split with respect to OpenCypher, the graph query language. The language itself is declarative, which leaves a lot of implementation freedom, but I'm curious if there is a Cypher algebra that can be identified that identifies the procedural operations that are implied by the Cypher declarative language.
Sure! While there isn’t a formalized “Cypher algebra,” we can enumerate the operations typically involved in a Cypher query’s execution plan. These operations are used by graph databases, like Neo4j, to implement Cypher queries procedurally. I’ll break these down into key categories for clarity:
- Pattern Matching Operations
These operations are core to graph traversal and pattern matching, which is central to Cypher queries.
• Expand: Traversing a relationship from one node to another. This operation follows relationships between nodes based on the match pattern.
• Expand(All): Expand across all relationships from a node.
• Expand(Into): Expand only along a relationship that hasn’t been traversed before (avoiding backtracking).
• Expand(Optional): Optionally match a relationship, returning null if no match is found.
• NodeByLabelScan: Scans all nodes of a particular label. This is often the starting point for a traversal when there’s no specific starting node.
• NodeIndexSeek: Uses an index to find nodes based on a property. This is akin to an index scan in relational databases.
• RelationshipByTypeScan: Scans relationships by their type, useful for matching specific relationship patterns.
• Expand(ShortestPath): Specific traversal logic for finding the shortest path between two nodes.
- Filtering and Conditional Operations
Filtering and restricting the results based on predicates (conditions).
• Filter: Applies a condition (such as WHERE) to restrict the set of nodes or relationships.
• Predicate Evaluation: Evaluates conditions based on node or relationship properties (e.g., n.age > 30).
• ExistenceCheck: Checks if a property or pattern exists.
• Distinct: Ensures unique results by filtering out duplicates.
• Limit: Limits the number of returned rows.
• Skip: Skips a defined number of rows from the result set.
- Join Operations
When matching multiple patterns, Cypher needs to combine results across different patterns.
• Cartesian Product: Combines two result sets in a cross-product fashion (typically undesirable unless intentional).
• Hash Join: A join operation that hashes one set of results and compares it to another.
• Nested Loop Join: A join operation that iterates through all elements in one set and matches it with elements in another set.
- Projection and Aggregation Operations
These operations deal with the transformation of data and the application of aggregations.
• Projection: Selects the properties or expressions to be returned.
• Return: Specifies which elements (nodes, relationships, properties) should be included in the result.
• With: Allows for projection between different query parts and pipelines results.
• Aggregation: Collects and aggregates data over groups.
• Collect: Aggregates results into a list.
• Count: Counts the number of matching elements.
• Sum: Sums numeric values.
• Avg: Calculates the average value.
• Min/Max: Finds the minimum or maximum value.
- Data Modification Operations
These operations are used in queries that modify the graph (e.g., creating or deleting nodes and relationships).
• Create: Adds new nodes or relationships to the graph.
• CreateNode: Creates a new node.
• CreateRelationship: Creates a new relationship between two nodes.
• Set: Assigns or updates properties on nodes or relationships.
• SetProperty: Updates or adds a property to a node or relationship.
• SetLabel: Adds a label to a node.
• Delete: Removes nodes or relationships.
• DeleteNode: Deletes a node (requires the node to have no remaining relationships).
• DeleteRelationship: Deletes a relationship.
• Remove: Removes labels or properties from nodes or relationships.
• RemoveLabel: Removes a label from a node.
• RemoveProperty: Removes a property from a node or relationship.
• Merge: A combination of MATCH and CREATE, it tries to match a pattern first and creates it if it doesn’t exist.
- Ordering and Paging Operations
These operations handle ordering and paging through results.
• Sort: Orders the result set based on a property or expression.
• Sort(Ascending/Descending): Specifies the direction of the sort.
• Skip: Skips a specified number of rows.
• Limit: Restricts the number of rows in the result set.
- Path and Subquery Operations
Operations for more complex path matching or handling subqueries.
• Pattern Comprehension: Extracts paths or expressions from the graph matching specific patterns.
• Subquery: Executes a subquery and integrates its result with the outer query.
- Union and Combination Operations
Operations for combining multiple result sets into one.
• Union: Combines the results of two or more queries into a single result set.
• Union All: Combines result sets without removing duplicates (contrast to Union, which removes duplicates).
- Other Operations
Various other useful operations.
• Unwind: Expands a list into individual rows, useful for iterating over collections in the result set.
• Call: Calls a stored procedure or a user-defined function (e.g., APOC procedures in Neo4j).
Summary of Operations:
• Pattern Matching: Expand, NodeByLabelScan, NodeIndexSeek, etc.
• Filtering: Filter, Distinct, ExistenceCheck, etc.
• Join: Cartesian Product, Hash Join, Nested Loop Join.
• Projection & Aggregation: Projection, Return, Collect, Count, Sum, etc.
• Data Modification: Create, Delete, Merge, Set, Remove.
• Ordering & Paging: Sort, Skip, Limit.
• Paths & Subqueries: Pattern Comprehension, Subquery.
• Combination: Union, Union All.
• Miscellaneous: Unwind, Call.
These operations are the procedural building blocks of a Cypher query’s execution plan and give insight into how the declarative nature of Cypher is translated into actual procedural operations in the graph engine. Each of these operations plays a role in efficiently traversing, filtering, and modifying the graph based on the user’s Cypher query. Apologies for the interruption! Let me continue from where we left off and elaborate on other operations that play a role in Cypher’s execution:
- Other Operations (continued)
These are miscellaneous operations that are useful in more specialized cases or to enhance query capabilities.
• Unwind: This operation is used to take a list and expand it into individual rows. For example, if you have a collection of elements and want to treat each one as a separate row in your result, UNWIND helps break that collection down. This is useful when dealing with arrays or sets within nodes.
• Example: UNWIND [1,2,3] AS x RETURN x would return each number in the list as a separate result.
• Call: This operation is used to invoke stored procedures or user-defined functions within the query. In Neo4j, you might frequently encounter procedures from the APOC library (a powerful set of extensions for Cypher).
• Example: CALL apoc.path.expandConfig is a stored procedure that can be used to explore nodes with specific configurations or constraints.
• Subquery Operations: In more recent versions of Cypher, subqueries allow the execution of a set of queries within a query block, isolating the execution of that inner query from the outer context. This can be useful for complex transformations or aggregations.
• Example: CALL { MATCH (n:Person) RETURN n.name } RETURN count(*) — this subquery runs a match inside a block and then counts the results.
• Schema Operations: These aren’t typically executed inside regular data queries but are part of managing graph schema structures.
• Create Index: Creates an index on a label and property, which can speed up query performance when matching nodes by that property.
• Drop Index: Removes an index.
• Create Constraint: Ensures uniqueness or enforces the existence of properties on certain labels.
• Drop Constraint: Removes a constraint from a label or relationship.
These operations play a vital role in extending the functionality of Cypher and enabling more complex queries, optimizations, and management of the underlying graph structure.
Summary of Miscellaneous Operations:
• Unwind: Turns lists into rows for more detailed processing.
• Call: Invokes stored procedures or user-defined functions to extend Cypher’s native capabilities.
• Subqueries: Isolates and encapsulates complex queries for intermediate transformations.
• Schema Operations: Manages graph schema with indexing and constraints.
I hope this breakdown gives you a more complete picture of all the operations at play in the “Cypher algebra” that underpins the execution of Cypher queries! Let me know if you’d like to explore any specific operation further.