Havel–Hakimi algorithm

The Havel–Hakimi algorithm is an algorithm in graph theory solving the graph realization problem. That is, it answers the following question: Given a finite list of nonnegative integers in non-increasing order, is there a simple graph such that its degree sequence is exactly this list? A simple graph contains no double edges or loops. The degree sequence is a list of numbers in nonincreasing order indicating the number of edges incident to each vertex in the graph. If a simple graph exists for exactly the given degree sequence, the list of integers is called graphic. The Havel-Hakimi algorithm constructs a special solution if a simple graph for the given degree sequence exists, or proves that one cannot find a positive answer. This construction is based on a recursive algorithm. The algorithm was published by Havel (1955), and later by Hakimi (1962).