Collection of reference networks

The reference PPI networks were obtained from Human Protein Reference Database (HPRD, Release 9)¹⁸ and Search Tool for the Retrieval of Interacting Genes/Proteins (STRING, Version 10)¹⁹. Six confidence levels (from 400 to 900 with step size of 100) of PPIs provided by STRING were considered separately, and were denoted as STRING400, STRING500, …, and STRING900. The summary statistics of proteins and interactions in the seven networks are listed in Table S1. Mathematically, we use a graph G = (V, E) to denote the reference PPI network comprised of a set of proteins V and a set of interactions E. Let A_n×n be the adjacency matrix of G, where n is the number of proteins. Clearly, the entry of A at row i and column j is 1 if protein i interacts with protein j; otherwise it is 0. The adjacency matrix A is column-wise normalized as