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I have a three-axis accelerometer that reads me its x, y, and z components. This results in three graphs. Is there a way to "combine" these components into one reading, hence, one graph? Same question holds for a gyroscope.

The datasheet for my device is here:

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The answer is: technically, yes, it is possible. The combined result is called Quaternion. This is what is typically used in 3D programs.

But most likely that is not what you had in mind.

Usually one can do a simplification and reduction of dimensions when in presence of some constraint.

Imagine that your moving object is bound to a planar surface: no matter how you tilt and rotate and pan it, it is still a 2D surface, plus a quaternion indicating the rototranslation.

But, once you have established the coefficients applied to the rototranslation, it is 2D.

Similar 1D case: imagine that your moving object is bound to some well-known geometrical shape, say a circumference. Once you have established how the circumference is oriented in the 3D space and its radius, you can express the position of your device by indicating either the angle or the distance from a reference point on the circumference.

In both cases you can simplify the representation because of constraints that do not allow for real 3d movement.

But if your device is a flying drone that can rototranslate freely within certain boundaries (max horizontal range, min/max altitude), there is no way that you can simplify the 3d coordinates.

If, instead, your question was related to the protocol used to read info from the accelerometer, you are bound to the protocol defined in the datasheet, by the manufacturer.

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