How threshold behaviour affects the use of subgraphs for network comparison

MOTIVATION A wealth of protein-protein interaction (PPI) data has recently become available. These data are organized as PPI networks and an efficient and biologically meaningful method to compare such PPI networks is needed. As a first step, we would like to compare observed networks to established network models, under the aspect of small subgraph counts, as these are conjectured to relate to functional modules in the PPI network. We employ the software tool GraphCrunch with the Graphlet Degree Distribution Agreement (GDDA) score to examine the use of such counts for network comparison. RESULTS Our results show that the GDDA score has a pronounced dependency on the number of edges and vertices of the networks being considered. This should be taken into account when testing the fit of models. We provide a method for assessing the statistical significance of the fit between random graph models and biological networks based on non-parametric tests. Using this method we examine the fit of Erdös-Rényi (ER), ER with fixed degree distribution and geometric (3D) models to PPI networks. Under these rigorous tests none of these models fit to the PPI networks. The GDDA score is not stable in the region of graph density relevant to current PPI networks. We hypothesize that this score instability is due to the networks under consideration having a graph density in the threshold region for the appearance of small subgraphs. This is true for both geometric (3D) and ER random graph models. Such threshold behaviour may be linked to the robustness and efficiency properties of the PPI networks.