title: Relationship between degree-rank function and degree distribution of protein-protein interaction networks.
abstract: It is argued that both the degree-rank function r=f(d), which describes the relationship between the degree d and the rank r of a degree sequence, and the degree distribution P(k), which describes the probability that a randomly chosen vertex has degree k, are important statistical properties to characterize protein-protein interaction (PPI) networks, both rank-degree plot and frequency-degree plot are reliable tools to analyze PPI networks. An exact mathematical relationship between degree-rank functions and degree distributions of PPI networks is derived. It is demonstrated that a power law degree distribution is equivalent to a power law degree-rank function only if scaling exponent is greater than 2. The puzzle that the degree distributions of some PPI networks follow a power law using frequency-degree plots, whereas the degree sequences do not follow a power law using rank-degree plots is explained using the mathematical relationship.
authors.affiliation: Department of Management, School of Information System and Management, National University of Defense Technology, Changsha, Hunan, PR China. wujunpla@163.com
authors.forename: Jun
authors.initials: J
authors.lastname: Wu
authors.forename: Yuejin
authors.initials: Y
authors.lastname: Tan
authors.forename: Hongzhong
authors.initials: H
authors.lastname: Deng
authors.forename: Dazhi
authors.initials: D
authors.lastname: Zhu
mesh_terms: D008954:Models, Biological; D011485:Protein Binding; D025941:Protein Interaction Mapping