Common Neighbors Extension of the Sticky Model for PPI Networks Evaluated by Global and Local Graphlet Similarity

The structure of protein-protein interaction (PPI) networks has been studied for over a decade. Many theoretical models have been proposed to model PPI network structure, but continuing noise and incompleteness in these networks make conclusions about their structure difficult. Using newer, larger networks from Sept. 2018 BioGRID and Jan. 2019 IID, we show the joint distribution of degree products and common neighbors has a greater impact on PPI edge connectivity than their individual distributions, and introduce two new models (CN and STICKY-CN) for PPI networks employing these features. Since graphlet-based measures are believed to be among the most discerning and sensitive network comparison tools available, we assess their overall global and local fits to PPI networks using Graphlet Kernel (GK). We fit 10 theoretical models to nine BioGRID networks and twelve Integrated Interactive Database (IID) networks and find: (1) STICKY and STICKY-CN are the overall globally best fitting models according to GK, (2) Hyperbolic Geometric Graph model is a better fit than any STICKY-based model on 4 species, (3) though STICKY-CN provides a better local fit than the STICKY model, the CN model provides the greatest local fit over most species. We conclude that the inclusion of CN into STICKY-CN makes it the best overall fit for PPI networks as it is a good fit locally and globally.