title: Are scale-free networks robust to measurement errors?
abstract: BACKGROUND
  Many complex random networks have been found to be scale-free. Existing literature on scale-free networks has rarely considered potential false positive and false negative links in the observed networks, especially in biological networks inferred from high-throughput experiments. Therefore, it is important to study the impact of these measurement errors on the topology of the observed networks.
  
  
  RESULTS
  This article addresses the impact of erroneous links on network topological inference and explores possible error mechanisms for scale-free networks with an emphasis on Saccharomyces cerevisiae protein interaction networks. We study this issue by both theoretical derivations and simulations. We show that the ignorance of erroneous links in network analysis may lead to biased estimates of the scale parameter and recommend robust estimators in such scenarios. Possible error mechanisms of yeast protein interaction networks are explored by comparisons between real data and simulated data.
  
  
  CONCLUSIONS
  Our studies show that, in the presence of erroneous links, the connectivity distribution of scale-free networks is still scale-free for the middle range connectivities, but can be greatly distorted for low and high connecitivities. It is more appropriate to use robust estimators such as the least trimmed mean squares estimator to estimate the scale parameter gamma under such circumstances. Moreover, we show by simulation studies that the scale-free property is robust to some error mechanisms but untenable to others. The simulation results also suggest that different error mechanisms may be operating in the yeast protein interaction networks produced from different data sources. In the MIPS gold standard protein interaction data, there appears to be a high rate of false negative links, and the false negative and false positive rates are more or less constant across proteins with different connectivities. However, the error mechanism of yeast two-hybrid data may be very different, where the overall false negative rate is low and the false negative rates tend to be higher for links involving proteins with more interacting partners.
authors.affiliation: Department of Mathematics, Washington University, St. Louis, MO 63143, USA. nlin@math.wustl.edu
authors.forename: Nan
authors.initials: N
authors.lastname: Lin
authors.forename: Hongyu
authors.initials: H
authors.lastname: Zhao
mesh_terms: D000465:Algorithms; D019295:Computational Biology / Q000379:methods*; D003198:Computer Simulation; D030562:Databases, Protein; D005656:Fungal Proteins / Q000737:chemistry; D016018:Least-Squares Analysis; D008954:Models, Biological; D016571:Neural Networks, Computer; D025941:Protein Interaction Mapping; D020543:Proteome; D040901:Proteomics; D015203:Reproducibility of Results; D012441:Saccharomyces cerevisiae / Q000378:metabolism; D029701:Saccharomyces cerevisiae Proteins / Q000378:metabolism; D012984:Software
chemical_list: D005656:Fungal Proteins; D020543:Proteome; D029701:Saccharomyces cerevisiae Proteins