I often state that business processes need complexity metrics and would like to share some facts behind that.
The first aspect addresses the complexity in documenting processes and the ability of humans to handle them.
There is a limited capacity of the human brain working memory. Quoting the Wikipedia article "the earliest quantification of the capacity limit associated with short-term memory was the "magical number seven" suggested by Miller in 1956" , see Wikipedia entry on working memory for full article.
So if you have a business process model with more than seven chunks in a single artifact, it is too complex for a normal human. The implication is that the modeler should group elements in chunks that pertain to a different modeling artifact, e.g; a subprocess, so that the working memory of the modeler can handle the complexity.
The second aspect is for business processes that are automated. Business processes is another form of expressing algorithmic and they are graphs with multiple paths and touch points. When you maintain such process and need to validate it, you have to ensure that you have tested all variations and paths. The turn around time to fix problems that may occur needs to stay within reasonable limits, otherwise the business process approach won't provide any advantages over classical coding. This is why a complexity metric that reflects the graph complexity and the turn around time to fix problem is necessary.
Both aspects imply that a complexity metric is defined when doing business process modeling, and that a complexity management method is defined. The method will have to give guidance for grouping elements in manageable chunks, that align with the enterprise organization as a chunk needs an owner, and that make sense from a functional standpoint.
In another blog entry I have mentioned the cyclomatic complexity and the control flow complexity as possible metrics. A way to manage complexity is to ensure that processes are modularized using one of the classification approaches described in the MIT process handbook.