As a key early artefact in the development of OO software, the quality of class diagrams is crucial for all later design work and could be a major determinant for the quality of the software product that is finally delivered. Quantitative measurement instruments are useful to assess class diagram quality in an objective way, thus avoiding bias in the quality evaluation process. This paper presents a set of metrics -based on UML relationships- which measure UML class diagram structural complexity following the idea that it is related to the maintainability of such diagrams. Also summarized are two controlled experiments carried out in order to gather empirical evidence in this sense. As a result of all the experimental work, we can conclude that most of the metrics we proposed (NAssoc, NAgg, NaggH, MaxHAgg, NGen, NgenH and MaxDIT) are good indicators of class diagram maintainability. We cannot, however, draw such firm conclusions regarding the NDep metric.