Cloth manipulation is very relevant for domestic robotic tasks, but it presents many challenges due to the complexity of representing, recognizing and predicting the behaviour of cloth under manipulation. In this work, we propose a generic, compact and simplified representation of the states of cloth manipulation that allows for representing tasks as sequences of states and transitions. We also define a Cloth Manipulation Graph that encodes all the strategies to accomplish a task. Our novel representation is used to encode two different cloth manipulation tasks, learned from an experiment with human subjects with video and motion data. We show how our simplified representation allows to obtain a map of meaningful motion primitives.