## 9.4. Operators

### Mathematical operators

The mathematical operators are `+`, `-`, `*`, `/` and `%`, `^`.

### Comparison operators

The comparison operators are `=`, `<>`, `<`, `>`, `<=`, `>=`, `IS NULL`, and `IS NOT NULL`. See the section called “Equality and Comparison of Values” on how they behave.

The operators `STARTS WITH`, `ENDS WITH` and `CONTAINS` can be used to search for a string value by it’s content.

### Boolean operators

The boolean operators are `AND`, `OR`, `XOR`, `NOT`.

### String operators

Strings can be concatenated using the `+` operator. For regular expression matching the `=~` operator is used.

### Collection operators

Collections can be concatenated using the `+` operator. To check if an element exists in a collection, you can use the `IN` operator.

### Property operators

 NoteSince version 2.0, the previously existing property operators `?` and `!` have been removed. This syntax is no longer supported. Missing properties are now returned as `NULL`. Please use `(NOT(has(.prop)) OR .prop=)` if you really need the old behavior of the `?` operator. — Also, the use of `?` for optional relationships has been removed in favor of the newly introduced `OPTIONAL MATCH` clause.

### Equality and Comparison of Values

#### Equality

Cypher supports comparing values (see Section 9.1, “Values”) by equality using the `=` and `<>` operators.

Values of the same type are only equal if they are the same identical value (e.g. `3 = 3` and `"x" <> "xy"`).

Maps are only equal if they map exactly the same keys to equal values and collections are only equal if they contain the same sequence of equal values (e.g. `[3, 4] = [1+2, 8/2]`).

Values of different types are considered as equal according to the following rules:

• Paths are treated as collections of alternating nodes and relationships and are equal to all collections that contain that very same sequence of nodes and relationships.
• Testing any value against `NULL` with both the `=` and the `<>` operators always is `NULL`. This includes `NULL = NULL` and `NULL <> NULL`. The only way to reliably test if a value `v` is `NULL` is by using the special `v IS NULL`, or `v IS NOT NULL` equality operators.

All other combinations of types of values cannot be compared with each other. Especially, nodes, relationships, and literal maps are incomparable with each other.

It is an error to compare values that cannot be compared.

### Ordering and Comparison of Values

The comparison operators `<=`, `<` (for ascending) and `>=`, `>` (for descending) are used to compare values for ordering. The following points give some details on how the comparison is performed.

• Numerical values are compared for ordering using numerical order (e.g. `3 < 4` is true).
• The special value `java.lang.Double.NaN` is regarded as being larger than all other numbers.
• String values are compared for ordering using lexicographic order (e.g. `"x" < "xy"`).
• Boolean values are compared for ordering such that `false < true`.
• Comparing for ordering when one argument is `NULL` is `NULL` (e.g. `NULL < 3` is `NULL`).
• It is an error to compare other types of values with each other for ordering.

### Chaining Comparison Operations

Comparisons can be chained arbitrarily, e.g., `x < y <= z` is equivalent to `x < y AND y <= z`.

Formally, if `a, b, c, ..., y, z` are expressions and `op1, op2, ..., opN` are comparison operators, then `a op1 b op2 c ... y opN z` is equivalent to `a op1 b and b op2 c and ... y opN z`.

Note that `a op1 b op2 c` does not imply any kind of comparison between a and c, so that, e.g., `x < y > z` is perfectly legal (though perhaps not pretty).

The example:

`MATCH (n) WHERE 21 < n.age <= 30 RETURN n`

is equivalent to

`MATCH (n) WHERE 21 < n.age AND n.age <= 30 RETURN n`

Thus it will match all nodes where the age is between 21 and 30.

This syntax extends to all equality and inequality comparisons, as well as extending to chains longer than three.

For example:

`a < b = c <= d <> e`

Is equivalent to:

`a < b AND b = c AND c <= d AND d <> e`

For other comparison operators, see the section called “Comparison operators”.