I have been working with "data science" related issues for almost a decade and I have always been huge fan of scale free networks and complexity theory.
When I am building a domain rich model (opposite of anemic machine learning model, which assumes that "logistic regression" or other general technical method is enough to solve the problem if I have enough data), I need to have mental model about the complexity and possible features related to the data domain. For this, the Model of Hierachical Complexity (Michael Commons) is useful; I should try to make layers of feature extractors, which operate on different levels of complexity. The lower layers sub-optimize agents to solve very specific problems very efficiently, and the layers above try to solve "noise pollution" generated from the conflicts of the interactions of lower layer agents.
I have discovered one efficient way to discover classes of hierarchical complexity by using scale-free network theory.
Let's take economy as an example. There are employees, organically grown companies, corporations funded by investments, banks and governments. When you take annual circulation of capital through each of these systems, you get logarithmic base numbers 4, 6, 32, 37 etc. Employees, who earn barely enough to be considered as employees (a dollar per day) rank to four on the logarithmic scale; world average is around 7 and very well paid Silicon Valley people are around 10. There seems to be strong correlates between 4 rated always being barely existing things, and 7 rated being average things; the rate of 10 seems to have quite much error, due to the "unfair advantages" aspects (I know this sounds horrific in mathematical exactness sense).
I have done similar research on music industry (based on Finnish data); for organically grown bands, there exists a base number, which quite well can determine, that if band barely exists (number 4), only 18 people have seen it during the year, for average organic bands the number is around 200 (rank 7) and it is really hard to remain unsigned when you reach over 1000 paying fans every year. For signed bands; in order to reach rank 7 you should tour at least 10 major city gigs (non-Arena, regular venues) a year with great success. With major labels; again very different game. Can this be just superstitious numerology or is this a thing?
So, it seems that scale free networks are everywhere and they seem to consist of entities, which depend on similar resources, but due to hierarchical complexity, have different rules of growth (fitness function). By using logarithmic scaling, it seems to be possible to vaguely detect these different complexity layers and which entities belong to which. I am not claiming that this method is of exact science, but for machine learning purposes, this would provide easy to use tool for multi-agent-system optimization.
I believe someone has already discovered this mathematical thing. I am looking for it's name in order to study it more deeply, since this problem has been fascinating me over a decade. Or is this one of those things, which are too hard to prove to exist aside from superstitions?