The main idea of software architecture is to concentrate on the "big picture" of a software system. In the context of object-oriented software systems higher-level architectural structures or views above the level of classes are frequently used to capture the "big picture" of the system. One of the critical aspects of these higher-level views is understandability, as one of their main purposes is to enable designers to abstract away fine-grained details. In this article we present a systematic mapping study on software metrics related to the understandability concepts of such higher-level software structures with regard to their relations to the system implementation. In our systematic mapping study, we started from 3951 studies obtained using an electronic search in the four digital libraries from ACM, IEEE, Scopus, and Springer. After applying our inclusion/exclusion criteria as well as the snowballing technique we selected 268 studies for in-depth study. From those, we selected 25 studies that contain relevant metrics. We classify the identified studies and metrics with regard to the measured artefacts, attributes, quality characteristics, and representation model used for the metrics definitions. Additionally, we present the assessment of the maturity level of the identified studies. Overall, there is a lack of maturity in the studies. We discuss possible techniques how to mitigate the identified problems. From the academic point of view we believe that our study is a good starting point for future studies aiming at improving the existing works. From a practitioner's point of view, the results of our study can be used as a catalogue and an indication of the maturity of the existing research results.

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