  Let $F$ be a probability distribution with support on the non-negative
integers. Four methods for generating a simple undirected graph with
(approximate) degree distribution $F$ are described and compared. Two methods
are based on the so called configuration model with modifications ensuring a
simple graph, one method is an extension of the classical Erd\H{o}s-R\'{e}nyi
graph where the edge probabilities are random variables, and the last method
starts with a directed random graph which is then modified to a simple
undirected graph. All methods are shown to give the correct distribution in the
limit of large graph size, but under different assumptions on the degree
distribution $F$ and also using different order of operations.
