When connecting the same data types together in a shading network the line will appear solid to indicate there is no conversion as in the 'string' connection below. If the data types are different, like in RGBA > Vector or RGB > RGBA below then the line appears as a broken line.
 

Shader output components are displayed on the VOP node, allowing component connections without the need for a conversion shader.
However, the following shaders allow more complicated conversions between data types: 

Float To Int

Converts a float into an integer value.

• Round: Rounds the input to the closest integer.
• Trunc: If the input is negative, this returns ceil(x), otherwise it returns floor(x).
• Floor: Returns the largest integer less than or equal to the input
• Ceil:  Returns the smallest integer greater than or equal to the input.

Float To Matrix

Compose a 4x4 matrix from 16 input components.

Float To RGB

Combine 3 floats into an RGB.

Float To RGBA

Combine 4 floats into an RGBA.

Matrix To Float

Extracts a component at the given column and row.

Int To Float

Converts an integer into a float value.

RGB To Float

Converts an RGB input to a float using the following modes

• min: Minimum component.
• max: Maximum component.
• average: Average of the RGB components.
• sum: Sum of the RGB components.
• luminance: Perceptual gray scale value as defined by Rec.709.

RGB To RGBA

Combine RGB and alpha inputs into an RGBA.

RGB To Vector

• raw: Passes the input through, does nothing.
• canonical: Converts the input from [0, 1] range to [-1, 1].

RGBA To Float

Combine an RGBA input to a float using the following modes

• min: Minimum component.
• max: Maximum component.
• average: Average of the RGB components.
• sum: Sum of the RGB components.
• luminance: Perceptual gray scale value as defined by Rec.709.

Vector To RGB

• raw: Passes the input through, does nothing.
• normalized: Normalizes the vector before converting the input from [0, 1] range to [-1, 1].
• canonical: Converts the input from [0, 1] range to [-1, 1].

Arnold Data Type Conversions

The following table shows how data types are converted within Arnold itself.