Is This for Real? Fast Graphicality Testing

One of the major advances in modeling networks is the realization that many of them (social, Internet, power grid, and so on) have predictable degree sequences-that is, the expected number of connections from a given node comes from some well-understood distribution. Models of these networks usually begin with random graphs whose degrees have the desired degree distribution. One task that repeatedly comes up in creating these model networks is testing whether a graph can even be created from a given integer sequence. Simply drawing a random sequence of integers from some distribution doesn´t guarantee that there even exists a graph with that degree sequence. When we have an integer sequence that can be realized as the degree sequence of some graph, we say that the sequence is graphic. While almost any graph theory book describes how a sequence can be tested to see if it´s graphic, surprisingly (because this testing has common applications), very little has been written about how to do it efficiently. This highlights the gap between simply knowing that a problem is theoretically tractable and being able to implement an efficient algorithm for practical use.