Relationship between degree-rank function and degree distribution of protein-protein interaction networks

  • Authors:

  • Jun Wu;Yuejin Tan;Hongzhong Deng;Dazhi Zhu

  • Affiliations:

  • Department of Management, School of Information System and Management, National University of Defense Technology, Changsha 410073, Hunan, PR China;Department of Management, School of Information System and Management, National University of Defense Technology, Changsha 410073, Hunan, PR China;Department of Management, School of Information System and Management, National University of Defense Technology, Changsha 410073, Hunan, PR China;Department of Management, School of Information System and Management, National University of Defense Technology, Changsha 410073, Hunan, PR China

  • Venue:
  • Computational Biology and Chemistry
  • Year:
  • 2008

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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.