When you take the action 'Add Child Incident' on a Parent Incident, the Child you add to the Parent automatically carries out the 'Add Parent Incident' action so the linking is made both ways.
Is there an action that is carried out on a child incident when you take the action 'Detach Child Incident' on a Parent? I can't seem to find one in the available actions list in Process Designer, but something must happen to the Child becuase when you take the 'Detach Child Incident' on a Parent, the Child looses it's relationship to the parent too
No, there is no complimentary "Detach Parent Incident" action available. When you perform the "Detach Child Incident" action the data is removed from the Incident Incident object completely. The reason that complimentary actions are required when adding Parent/Child links is to enable a level of control over which Incidents can become children and parents. Once an Incident is a child it is up to a User who has the privilege (and presumably therefore the authorisation) to decide to remove that child from a parent - it's a different kind of control.