Graph exploration and editing are still mostly considered independently and systems to work with are not designed for todays interactive surfaces like smartphones, tablets or tabletops. When developing a system for those modern devices that supports both graph exploration and graph editing, it is necessary to 1) identify what basic tasks need to be supported, 2) what interactions can be used, and 3) how to map these tasks and interactions. This technical report provides a list of basic interaction tasks for graph exploration and editing as a result of an extensive system review. Moreover, different interaction modalities of interactive surfaces are reviewed according to their interaction vocabulary and further degrees of freedom that can be used to make interactions distinguishable are discussed. Beyond the scope of graph exploration and editing, we provide an approach for finding and evaluating a mapping from tasks to interactions, that is generally applicable. Thus, this work acts as a guideline for developing a system for graph exploration and editing that is specifically designed for interactive surfaces.