Graph question - How to compute scaling parameter α after gaining a degree sequence of a graph?

Question

I am a junior data scientist and very new to the graph theory, so I guess my question is stupid. Recently, I have been reading several papers related to a graph theory to try to answer a question that whether my network data (two columns: first column is about 18,500 unique words in a book, and the second column is the frequency of each of those words occurring in that book) is scale-free or not? In those papers, they told me that, their first step involving finding a degree sequence of that graph. OKE, I turned my data into adjancy matrix and computed degree sequence of the data. Then, they fit the model to choose kmin and then seek scaling parameter α based on the optimal kmin. The method they choose kmin via the standard Kolmogorov-Smirnov minimization approach. So what place is my degree sequence used?