Connectivity is the basis of several methodological concepts in mathematical morphology. In graph-based approaches, the notion of connectivity can be derived from the notion of adjacency. In this preliminary work, we investigate the effects of relaxing the symmetry property of adjacency. In particular, we observe the consequences on the induced connected components, that are no longer organised as partitions but as covers, and on the hierarchies that are obtained from such components. These hierarchies can extend data structures such as component-trees and partition-trees, and the associated filtering and segmentation paradigms, leading to improved image processing tools.