In the analysis of large-scale network data, a fundamental operation is the comparison of observed phenomena to the predictions provided by null models: when we find an interesting structure in a family of real networks, it is important to ask whether this structure is also likely to arise in random networks with similar characteristics to the real ones. A long-standing challenge in network analysis has been the relative scarcity of reasonable null models for networks; arguably the most common such model has been the configuration model, which starts with a graph G and produces a random graph with the same node degrees as G. This leads to a very weak form of null model, since fixing the node degrees does not preserve many of the crucial properties of the network, including the structure of its subgraphs.

There is inherent information captured in the order in which we write words in a list. The orderings of binomials — lists of two words separated by ‘and’ or ‘or’ — has been studied for more than a century. These binomials are common across many areas of speech, in both formal and informal text. In the last century, numerous explanations have been given to describe what order people use for these binomials, from differences in semantics to differences in phonology. These rules describe primarily ‘frozen’ binomials that exist in exactly one ordering and have lacked large-scale trials to determine efficacy.