How good is the overlap between two biological networks?

Unlike in physics where experimental results are compared to theoretical models, a biological signal is often detected by comparing to a negative benchmark. As an example, the signal content of biological networks (e.g. protein-protein interactions) is traditionally highlighted by showing significant overlap with a gold standard network. Significance is then assessed by comparison with a negative benchmark in which the gold standard network is randomized. Although a significant difference from the negative benchmark indicates the presence of signal, the low observed overlap between most biological networks questions the quality of these networks. Thus, a positive benchmark is needed to quantify how much a network agrees with a gold standard network. Here, we propose such a positive benchmark that captures a best-case scenario by creating an alternative network ensemble. The alternative networks contain only the links of the union of the two networks and preserve the original degree sequence, based on the maximum entropy framework. The negative and positive benchmarks together allow us to normalize the observed overlap of two networks. As an application, we compared the molecular and functional networks in yeast as well as in human, leading to an agreement network of networks for each organism. Our results show that most networks of a given organism agree well with each other despite the low observed overlap, providing insights for network data integration as well as assessing new network datasets.