# 4.9. TQL Constraints on Graph Elements¶

We have discussed how to express the topological part of a TQL query using structures. We now discuss how to express constraints on the data stored in the components of the graph.

Recall that each graph component in xGT has an associated schema with named properties. Each property in the schema has an associated data type (see Data Types and Operators in xGT).

Constraints on the properties of the graph elements are described in the WHERE clause of a TQL query. The WHERE clause consists of expressions involving the properties of the graph elements, combined with constants (of the appropriate data type) and commonly used comparison, arithmetic, and boolean operators.

The combination of the structure and constraints in a query is called the graph pattern in TQL.

Properties are referred to by using the `.` (dot) operator in between the name of a bound variable and the name of a property: `a.name` would access the property named `name` of the graph element bound to the variable `a`.

Property expressions can be combined with other property expressions and constants using TQL’s Cypher operator subset.

Supported operators are as follows:

• Arithmetic: `+`, `-`, `*`, `/`, `^` (exponentiation), `%` (modulus), (unary) `-`

• Boolean: `AND`, `OR`, `XOR`, `NOT`

• Comparison: `=` (equality), `<>` (difference), `<`, `>`, `<=`, `>=`, `IS NULL`, `IS NOT NULL`

• String: `STARTS WITH`, `ENDS WITH`, `CONTAINS`, `+` (concatenation operator).

• List: `IN` (membership test), `+` (list concatenation), `[ ]` (subscripting and slicing operators).

Constants are supported for the following data types:

• Integer numbers

• Floating-point numbers (32 bit)

• Boolean true and false

• String constants (surrounded by double or single quotes)

• Null constant (`NULL`)

• Dates

• Times

• Datetimes

• Lists

Parentheses `()` can be used to indicate precedence when dealing with nested expressions.

Examples of WHERE constraints are as follows:

```WHERE p.name = "John" AND p.age < 40
```
```WHERE c.value > 10.0 OR c.value < 2.5
```
```WHERE (p.name STARTS WITH "D" OR p.name STARTS WITH "F") AND p.address IS NOT NULL
```
```WHERE c.time > 20 AND (c.value > 10.0 OR c.value < d.value) AND c.`co\$t` < 10.0
```

## 4.9.1. Pattern Filters¶

In addition to constraints on property values, TQL allows for constraints that filter on the existence (or non-existence) of linear graph patterns connected to the main topological structure of the query. The expression `WHERE <linear graph pattern>` evaluates to a boolean true value if the pattern exists in the graph, false if it does not. The linear graph pattern is expressed as a sequence of vertex-edge-vertex steps that must start and end with a vertex, subject to the same rules as the expression of the topological structure of the query. We use the term “pattern filter” to denominate this type of topological pattern checks. Examples of pattern filters are as follows:

• `WHERE (a)-[]->(a)` to check that the matched vertex `a` has a one edge cycle.

• `WHERE NOT (a)-[]->(a)` to check that the matched vertex `a` does NOT have a one edge cycle.

• `WHERE a.year >= 1990 AND (a)-[: WorksWith]->(b)` to check that person `a` was born after the year 1990 and also works with person `b`, both of which must be matched in the main structure of the query.

In TQL, pattern filters are restricted to one linear chain of graph steps (that is the pattern cannot be a non-linear pattern connected by the comma operator). Each vertex or edge step in the linear chain can either have a variable or not. If it has a variable, it must be a variable that is the same as one attached to an existing topological step in the main query structure. New variables are not allowed to be introduced in pattern filters.

A frame name can be provided by the query to indicate which frame the pattern filter step binds to: e.g. `(: Vertex)` or `(a : Vertex)`.

In addition to frame information, it is possible to specify equality constraints on the matched properties via the use of a property map. The use of property maps for constraints inside a pattern filter is useful on graph steps that do not bind to a previously matched variable. Examples of the use of property maps in pattern filters are as follows:

• `WHERE (a)-[{ value : 10 }]->(a)` will check that the matched vertex `a` is connected in a one-step cycle to itself via an edge that has the property `value = 10`.

• `WHERE ({ key : b.key + 10 })-[]->()-[]->(a)` will check the existence of a two edge path that ends in the matched vertex `a` and starts on a vertex with a key property greater by 10 than the key property of a matched vertex `b`.

Note that adding property map constraints on a step with an existing variable could easily lead to empty answers. For example, in the pattern `WHERE (a { a.key : 10 })-[]->()` if the matched key property for `a` is not 10, then the constraint will be false. This happens because property maps only allow the expression of equality constraints.

A full example of the use of a pattern filter is as follows:

```MATCH (a)-[]->(c)<-[]-(b)
WHERE a <> c AND ({ key : b.key + 10 })-[]->(a)
```

In this case, the topological structure indicates that vertices a and b each have an edge connecting them to vertex c. In addition, the constraints indicates that a and c must be different and that there must be another vertex with a key value of the key of b plus ten that has an edge connecting it to a. As can be seen in this case, the pattern filter check is an extension of the topological structure represented in the match pattern.

## 4.9.2. Functions¶

TQL provides a set of functions that can be used in queries. These functions include standard Cypher functions and a few that are unique to TQL.

### 4.9.2.1. Aggregation Functions¶

Sometimes it is useful to know cumulative information about results. Aggregation functions provide this ability by combining results from multiple rows into a single result. For instance, the following query returns a single row that has the total number of executives in all the companies in the graph:

```MATCH (c:Companies)
RETURN sum(c.num_executives)
```

In addition to a single cumulative result, rows can be grouped by user-specified keys. The grouping keys are non-aggregated expressions that are given alongside the aggregation function expressions. Input rows with the same value for the grouping keys are combined.

Consider the example where the `Companies` frame has a column `state` indicating which state the company headquarters is located in. The following query returns a single row for each unique value of state along with the total number of executives in each state:

```MATCH (c:Companies)
RETURN c.state, sum(c.num_executives)
```

There can be multiple grouping keys and aggregation functions. Consider this example that groups results by the unique combinations of city and state:

```MATCH (c:Companies)
RETURN c.state, c.city, sum(c.num_executives), avg(c.num_executives)
```

The `DISTINCT` keyword can be used in conjunction with an aggregation function. Using `DISTINCT` with an aggregation function generates the unique set of input values for the aggregation function, and the function is applied to the set of distinct values instead of all the values.

For example, consider this query that returns the number of unique cities that company headquarters are located in:

```MATCH (c:Companies)
RETURN count(DISTINCT c.city)
```

The following aggregation functions are supported by TQL:

Aggregation Functions

Name

Description

count(*)

Returns the number of elements in the results set.

count(expr)

Returns the number of non-null values of an expression in the results set.

avg(expr)

Returns the numerical average of all values of an expression in the results set.

sum(expr)

Returns the sum of all values of an expression in the results set.

min(expr)

Returns the smallest of all values of an expression in the results set.

max(expr)

Returns the largest of all values of an expression in the results set.

collect(expr)

Returns a list containing all values of an expression in the results set.

The variant `count(*)` includes `null` values in the count while the variant `count(expr)` excludes expressions that evaluate to `null`. For all other aggregation functions, expressions that evaluate to `null` are excluded from the result. The functions `avg()` and `sum()` take the argument `expr` that is an expression that evaluates to either integer or float type and return an aggregate value of the same type as `expr`. Expressions that evaluate to any other type result in an error. The functions `min()` and `max()` take the argument `expr` that is an expression that evaluates to any type and return an aggregate value of the same type as `expr`.

The aggregation functions can only be used in RETURN and WITH expressions.

Examples of their usage are as follows:

```RETURN count(*) AS total
```
```RETURN avg(a.age)
```
```WITH sum(p.sale_price - p.production_cost) AS profit
```
```WITH max(a.dob) AS youngest, min(a.dob) AS oldest, count(DISTINCT a.dob) AS unique_dobs
```

### 4.9.2.2. Conversion Functions¶

Conversion functions allow converting one type into a different type, for instance converting an integer into a string. TQL supports the following conversion functions:

Conversion Functions

Name

Description

toBoolean(expr)

Converts the given expression to a bool.

toInteger(expr)

Converts the given expression to an integer.

toFloat(expr)

Converts the given expression to a IEEE 754 float representation.

toString(expr)

Converts the given expression to a string.

The conversion functions take the single argument `expr` and can be applied to properties and expressions of any type. They can be used in any context where an expression is valid, including WHERE, RETURN, WITH, CASE, ORDER BY, CREATE, MERGE and SET expressions.

The `toBoolean()` function will convert strings to boolean. Strings can be 0, 1, true, or false. True and false are case-insensitive. Other types used in conversion besides boolean or string will result in an error.

The `toInteger()` function will truncate floats and convert booleans to 0 or 1 for false and true, respectively. IPv4 addresses are converted to their integer representation. Date and datetime types are converted to seconds since the epoch where a date type is considered to occur at midnight. The function converts time types to seconds since midnight. Strings are parsed and converted to integers, if possible. When parsing a string, the function expects a format similar to Neo4j where the string value can be written as positive or negative integer with an optional decimal fractional part that will be truncated.

The `toFloat()` function works similarly to `toInteger()`, but will use 32-bit IEEE 754 float precision. For time and datetime types, the fractional precision of the seconds will be represented in the float. Some considerations may need to be taken given that 32-bit floats have precision relative to magnitude. For more recent dates this precision can be 10 to 10^2 given the magnitude because the seconds since the epoch can be fairly large. This means the precision will be seconds to tens of seconds. Similar precision may be expected from IP addresses given that each value in the upper range represents 256^3.

If `toBoolean()`, `toFloat()`, or `toInteger()` fails at parsing a string, they will return a null.

The conversion functions can be used in any context where an expression is valid, including WHERE, RETURN, WITH, CASE, ORDER BY, CREATE, MERGE and SET expressions.

Some examples are:

```WHERE toString(a.property) = "5"
```
```WITH toString(10.5 + a.float_property) AS aString
```
```RETURN toInteger(10.5 + a.float_property) AS anInt
```

### 4.9.2.3. Mathematical Functions¶

TQL supports the following mathematical functions:

Mathematical Functions

Name

Description

abs(expr)

Returns the absolute value of an expression.

ceil(expr)

Returns the ceiling of an expression.

floor(expr)

Returns the floor of an expression.

rand()

Returns a random floating point number in the range of 0 (inclusive) to 1 (exclusive).

round(expr)

Returns the rounded value of an expression.

sign(expr)

Returns 0 if the value of the expression is zero, 1 if positive, and -1 if negative.

The function `rand()` takes no arguments. The other mathematical functions take the argument `expr` that must be an expression that evaluates to either an integer or float type and return a value of the same type as the input expression. If `expr` evaluates to `null`, `null` is returned. Using these functions on any non-numeric type results in an error.

The mathematical functions can be used in any context where an expression is valid, including WHERE, RETURN, WITH, CASE, ORDER BY, CREATE, MERGE and SET expressions.

### 4.9.2.4. String Functions¶

TQL supports the following string functions:

String Functions

Name

Description

reverse(string)

Returns a string with the elements of the passed-in parameter in reverse order.

size(string)

Returns the number of characters in the string.

substring(orig, start [,length])

Returns a substring of the original string.

The `substring()` function has two required arguments and a third optional argument. The argument `orig` is an expression that evaluates to a string to operate on. The argument `start` is an expression that evaluates to a 0-based starting position in the original string. The optional argument `length` is an expression that evaluates to the length of the substring to extract. If `length` is not given, the function returns the substring beginning at `start` through the end of `orig`. If `orig` evaluates to `null`, `null` is returned. If `orig` evaluates to any non-string type, an error is thrown. If `start` or `length` evaluates to either a negative integer or `null`, an error is thrown. If `start` or `length` evaluates to any non-integer type, an error is thrown.

The string functions can be used in any context where an expression is valid, including WHERE, RETURN, WITH, CASE, ORDER BY, CREATE, MERGE and SET expressions.

### 4.9.2.5. List Functions¶

TQL supports the following list functions:

List Functions

Name

Description

range(start, stop [,step])

Returns a list containing a range of integer values.

reverse(list)

Returns a list with the elements of the passed-in parameter in reverse order.

size(list)

Returns the number of elements in the list.

tail(list)

Returns a list that does not include the first element in the passed-in parameter.

keys(variable)

Returns a list of the properties associated with the bound variable passed in as a parameter.

The `range()` function generates an inclusive range. The function has two required arguments and a third optional argument all of which must be integer expressions. The argument `start` is the first integer included in the resulting range. The argument `stop` is the last value potentially included in the resulting range. The argument `step` indicates the difference between subsequent elements in the list. If `step` is not given, its default is `1`. Note that `stop` may not be included in the list because of the step size.

The `keys()` function must be passed a bound variable associated with a frame.

The following Cypher functions for list are not currently supported by xGT: `labels()`, `reduce()`, `toBooleanList()`, `toFloatList()`, `toIntegerList()`, and `toStringList()`.

### 4.9.2.6. Path Functions¶

TQL supports the following functions that can be applied to path variables (see Path Variable Capture):

Path Functions

Name

Description

length(p)

Returns the number of edges contained in the path variable.

nodes(p)

Returns a list with the vertices that were traversed in the path p.

relationships(p)

Returns a list with the edges that were traversed in the path p.

Path variables and lists are not compatible with each other. Functions that can be applied to lists cannot be applied to path variables and vice versa. The path functions nodes() and relationships() return lists of vertices and edges, but those lists are not considered paths.

Both the nodes() and relationships() return the list of vertices and edges in the order in which they appear in the path. The path itself stores vertices and edges in the order in which they appear in the TQL query written by the user, independent of query reordering and optimization.

### 4.9.2.7. Degree Functions¶

TQL supports the following degree functions:

Degree Functions

Name

Description

indegree(vertex [, edge_frame])

Returns an integer value with the number of incoming edges to the specified bound vertex variable. Can be global or relative to a particular edge frame.

outdegree(vertex [, edge_frame])

Return an integer value with the number of outgoing edges from the specified bound vertex variable. Can be global or relative to a particular edge frame.

The degree functions have one required and one optional argument. The argument `vertex` must be a bound variable to a vertex component in the structure. The optional second argument `edge_frame` must be the qualified name of an edge frame in xGT. Any other values for `vertex` or `edge_frame` results in an error.

Degree computations without the optional edge frame name are global, in the sense that the degree of the bound vertex is computed across edge frames incident on the owning vertex frame in xGT. When using the optional edge frame name argument, the degree computation becomes relative to that particular edge frame. That is, the degree of the vertex is computed only for edges of the named frame.

The degree functions can be used in any context where an expression is valid, including WHERE, RETURN, WITH, CASE, ORDER BY, CREATE, MERGE and SET expressions.

Examples are as follows:

```WHERE indegree(a) = 10
```
```WHERE outdegree(b) > 10
```
```WHERE (outdegree(c, FriendOf) + outdegree(c, WorksFor)) < 5
```

### 4.9.2.8. Function to Enforce Distinct Vertices¶

By default xGT and TQL do not impose restrictions on the identity of the vertices and edges in a structure. In particular, cycles are allowed (graph paths from one vertex to the same vertex) and will be reported if present in the data. There are cases where the identity of the vertices in a query is not important, but there are also cases in which at least some of the vertices must be different from each other.

It is easy to express distinct vertices with just two: `a <> b`, but if we have more – say `a`, `b`, `c` and `d` – then expressing all the pairwise constraints becomes tedious and error-prone: `a <> b AND a <> c AND a <> d AND b <> c AND b <> d AND c <> d`. For this reason, TQL provides a shortcut:

Unique Vertices Function

Name

Description

unique_vertices(vertex_list)

Enforces that a set of vertices are all distinct.

The function `unique_vertices()` takes a list of bound vertex variables. Any other input value results in an error. It can only be used as part of a WHERE clause with its arguments being the bound variables for vertices that must be distinct from each other. xGT automatically generates all the necessary constraints and adds them to any other user-provided constraints in the query.

## 4.9.3. Constant Expressions¶

xGT and TQL support expressing numerical and string constants directly in a query. TQL also provides mechanisms for expressing constraints based on date, time, datetime, and IPv4 address types. The functions `date()`, `time()`, `datetime()` and `ipaddress()` let the TQL query represent constants of the corresponding types built from string expressions in an appropriate format.

The following are the formats that are supported for each constant type:

• `date()`: The string must be in the format `YYYY-MM-DD`.

• `time()`: The string must be in the format `HH:MM:SS` or `HH:MM:SS.S` where the fractional part must be at least 1 digit, but no more than 19 digits (will be rounded to 6 digits). Time zones are supported as input but will be converted to Coordinated Universal Time (UTC) and the time zone will not be retained. Time zones are represented as either `Z` for UTC or by an offset containing an hour part and optional minute part. The hour part must be between 14 and -14 and the minute part must be in 15 minute increments. Valid formats are `HH:MM:SSZ`, `HH:MM:SS+HH:MM`, `HH:MM:SS-HH:MM`, `HH:MM:SS+HH`, and `HH:MM:SS-HH`.

• `datetime()`: The string must be in the format of a date followed by a time separated by either a `T` or a space. The date and time must follow the formats given above. Examples of valid formats are `YYYY-MM-DDTHH:MM:SS`, `YYYY-MM-DD HH:MM:SS.µµµµµµ`, `YYYY-MM-DDTHH:MM:SS.µµµµµµ+HH:MM`.

• `ipaddress()`: The string must be in the format `NUM.NUM.NUM.NUM` where each dot-separated value is a number between 0 and 255.

Examples of the use of these constant expressions are as follows:

```WHERE a.date > date("2018-01-01")
```
```WHERE a.time = time("16:00:00.000000")
```
```WHERE b.datetime <> datetime("2017-12-31T00:00:00")
```
```WHERE b.ipaddr = ipaddress("192.168.1.1")
```

Note that `=`, `<>`, `>`, `<`, `>=` and `<=` operators are supported for date, time, and datetime properties and constants. However, IPv4 addresses only support `=` and `<>` comparisons.

## 4.9.4. CASE Expressions¶

xGT and TQL support the CASE clause which provides conditional expressions. There are two types of CASE expressions: simple and generic. The simple form compares values to a test expression while the generic form evaluates a series of conditional expressions.

CASE expressions can be used in any context where an expression is valid, including WHERE, RETURN, WITH, CASE, ORDER BY, CREATE, MERGE and SET expressions.

### 4.9.4.1. Simple CASE Expressions¶

The simple CASE expression has the following form:

```CASE test
WHEN value THEN result
[WHEN value THEN result]
[ELSE default]
END
```

Each of test, value, result, and default are expressions. The list of values is compared against the test expression in order until one is found that is equal to the test expression. If a value is found equal to the test expression, the result associated with that value is returned. If no value is equal to the test expression, the default is returned. If no value is equal to the test expression and no default is given, null is returned.

All the result expressions and the default expression must be of the same type. The test expression and all the value expressions must be of the same type.

### 4.9.4.2. Generic CASE Expressions¶

The generic CASE expression has the following form:

```CASE
WHEN predicate THEN result
[WHEN predicate THEN result]
[ELSE default]
END
```

Each of test, predicate, result, and default are expressions. The list of predicates is evaluated in order until one is found true. If a predicate is found true, the result associated with that predicate is returned. If no predicate is true, the default is returned. If no predicate is true and no default is given, null is returned.

All the result expressions and the default expression must be of the same type. All the predicate expressions must be of boolean type.

### 4.9.4.3. Examples¶

This example uses a simple case expression in a RETURN clause:

```MATCH (v:VertexFrame)
WHERE v.ID < 10
RETURN v.ID,
CASE v.ID
WHEN 2 THEN 1
ELSE 0
END AS result
```

The example returns a row for each vertex with an ID < 10 containing two columns. The first column is the ID. The second column is 1 if the ID is 2 and 0 otherwise.

This example uses a generic case expression in a WITH clause:

```MATCH (v:VertexFrame)
WHERE v.ID < 10
WITH v,
CASE
WHEN v.ID % 2 = 1 THEN "odd"
ELSE "even"
END AS type
WHERE type = "even"
RETURN v.ID
```

The example returns a row for each vertex with an even ID less than 10 with a single column holding the ID.

## 4.9.5. Cypher Parameters¶

xGT and TQL support user-defined parameters indicated in a query by a variable name starting with `\$`. The values of the parameter are supplied via a Python map at the time of running or scheduling a job via `run_job()` or `schedule_job()`.

Cypher parameters can be used in the following ways:

• For literals and expressions:

```MATCH (c:Companies)
WHERE c.num_executives >= \$param
```
```conn.run_job(query, parameters = { "param": 10 })
```

Python boolean, float, integer, and string types are automatically converted to the appropriate Cypher type. Non-nested lists of these types are also supported. If the parameters are intended to be date, time, datetime, or ipaddress, one must use the appropriate casting function on the parameter in the query itself:

```MATCH (c:Companies)
WHERE c.date_founded = DATE(\$date)
```
```conn.run_job(query, parameters = { "date": "2019-02-10" })
```

Lists cannot be cast to these types, but elements in a list can be individually cast to these types.

• String pattern matching:

```MATCH (c:Companies)
WHERE c.company_name STARTS WITH \$name
```
```conn.run_job(query, parameters = { "name": "Trov" })
```
• In the creation of an object:

```CREATE (c:Companies { company_name : \$name, date_founded: DATE(\$date) })
```
```conn.run_job(query, parameters = { "name": "NewCompany", "date": "2021-01-01" })
```
• In the setting of object properties:

```MATCH (c:Companies)
WHERE c.company_name = "NewCompany"
SET c.num_executives = \$param
```
```conn.run_job(query, parameters = { "param": 10 })
```
• For skip and limit values:

```MATCH (c:companies)
WHERE c.num_executives >= 10
RETURN c
SKIP \$s
LIMIT \$l
```
```conn.run_job(query, parameters = { "s": 10, "l": 5 }
```