Counting and selecting at random bipartite graphs with fixed degrees

The paper first recalls the bijective mapping between bipartite simple graphs with specified degrees and 0/1 arrays with fixed sums of rows and columns, and these graphs are counted, using an enumerative procedure. Tables that contain the numbers of such graphs with at most 10 edges are given. Then a total order is put on this set, and an algorithm is provided to build the graph that has a given rank. If this rank is selected at random, uniformly or not, a random bipartite simple graph is obtained.