Complexity is defined as function of interdependency (structure) and uncertainty (entropy). It represents on one side the degree of functionality a system can have, using the term "system" as an abstract term which can stand for macroeconomic environments like countries or markets, companies, division, customer groups, providers, processes like supply chains or sales cycles or even living beings. In order to fulfill a certain task, a system needs to have a certain minimum degree of complexity, otherwise it is not able to fulfill the desired function.

Examples for low complexity:

A system that needs to calculate what is represented by the program "output 1 + 1."

A company that cuts potato into pieces or a dealing with ticket machine that sells one single type of ticket for the price of 1 coin of 1 Euro .

Examples for more complex systems: 

A system that supports a large corporation in an integrated way for sales, accounting, purchasing , treasury management, supply chain management and planning, project managent and other aspects and processes.

A company that produces a huge product portfolio from electric toasters to atomic plants.

Beyond that minimum degree of complexity additional complexity can be added to the system consciously or by evolution. The above mentioned example program can be rewritten to "output (sqrt(16) - 4cos(sin(0)) + 4)/(7 modulo 5)". Both do the same but the second program includes unnecessary complexity and thus it is harder to handle, understand or altered.

The same is valid for companies. Companies can run with additional complexity on top of the minimum one, making their management more complicated to be understood holistically and therefore less predictable and less resilient to effects from the environment in which they operate. 

The recent development of economic history shows that the systemic risks have increased and that the environment in which companies operate have become highly unpredictable. This increase of uncertainty increases the fragility of the companies, making it more and more difficult to be prepared for critical or life threatening change.

Therefore it is of a very high interest to reduce the amount of unnecessary complexity as it directly increases the fragility if the evolution of the environment a system operates in is highly uncertain. Consequently risk is related to (unnecessary) complexity, especially as it can be "homemade". The mission of complexity analysis is finding out

A: The degree of complexity, and entropy within a system

B: Which variables are the ones that add most to the overall complexity and which have the highest impact on the system if they change.

The variables determined as significancant after having realized the complexity analysis are by nature factors of risk as if they change a change to the system will occur. If their contribution to the total complexity can be reduced, the system will reduce in complexity and consequently it will gain more resilience.

Business structure map of one of the three rating agencies, measured by Ontonix.

More details can be found here.