Sorry for a possibly off-the-topic question, but I am afraid to gain the necessary overview to give an answer (supposed the question is not ill-posed) is beyond my capabilities.

In the course of creating random graphs I got to know the concept of generating functions for statistical distribution (as thoroughly described in Luc Devroye's book Non-uniform Random Variate Generation). Such functions are necessary to create given degree sequences to produce configuration model random graphs.

On the other side I learned to know that generating functions (in the sense of generatingfunctionology) can help to calculate combinatorial properties of graphs, especially random graphs.

So I wonder if there is some "deep" connection between both kinds of generating functions. Both have to do with statistics resp. combinatorics of graphs. Can knowing one help to know the other?

Sorry for a possibly off-the-topic question, but I am afraid to gain the necessary overview to give an answer (supposed the question is not ill-posed) is beyond my capabilities.

In the course of creating random graphs I got to know the concept of generating functions generators for statistical distributions (as thoroughly described in Luc Devroye's book Non-uniform Random Variate Generation). Such functions (as algorithms) are necessary to create given degree sequences to produce configuration model random graphs.

On the other side I learned to know that generating functions (in the sense of generatingfunctionology) can help to calculate combinatorial properties of graphs, especially random graphs.

So I wonder if there is some "deep" connection between both kinds of "generating functions". Both have to do with statistics resp. combinatorics of graphs. Can knowing one help to know the other?