The Havel-Hakimi algorithm determines whether a given degree sequence is graphical or not, i.e., whether a simple graph can be constructed from the values. The algorithm was first published by Havel in 1955, and later by Hakimi in 1962.
A useful step-by-step run-through of the algorithm trace is available to view as the accepted answer in this question.
Two versions of the program are available in the repository. The original version was written in late 2018 and is available as Havel_Hakimi.java, while the updated code is available as two files in the HavelHakimi_2022 folder.
Compile the code by entering the parent directory and running javac Havel_Hakimi.java or javac HavelHakimi.java Main.java. The code can then be run via java Havel_Hakimi or java Main DEGREE_SEQUENCE.
The original version of the code uses a Scanner to retrieve the input degree sequence, while the updated version uses a command-line argument in the format of: n,n,n,n...etc up until a total of 10 elements.