The skeleton is an effective tool for shape analysis if its structure can be regarded as a faithful stick-like representation of the pattern. However, contour noise may affect this structure by originating spurious skeleton branches, so that skeletonization algorithms should include a pruning phase devoted to an analysis of the peripheral skeleton branches and, possibly, to their partial or total removal. In this paper, labeled skeletons are considered and the significance of a peripheral branch is evaluated by analyzing the type of interaction between the pattern subset corresponding to the peripheral branch and the pattern subsets corresponding to the skeleton branches adjacent to the peripheral branch. The proposed criteria for skeleton pruning are expressed in terms of four parameters, which as a whole describe the role that the pattern subset corresponding to the peripheral branch plays in the characterization of the shape of the pattern.