Modularity, reuse, and hierarchy: Measuring complexity by measuring structure and organization

To develop better complexity measures, a reasonable approach is to base them on those principles of design that designers use. Modularity, reuse and hierarchy (MR&H) have been identified by engineers as useful principles for designing complex systems, and these characteristics can be seen in Nature. Here we develop metrics for each of MR&H, and then use them to develop several metrics of structure and organization. Further, we propose to evaluate complexity measures both empirically and on a set of abstract object-construction examples. After applying these tests to a handful of previously defined complexity measures, as well as ones we define here, we find that only two of our measures pass both sets of tests.