On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
A random graph model for massive graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The degree sequence of a scale-free random graph process
Random Structures & Algorithms
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Random Structures & Algorithms
Stochastic models for the Web graph
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Random Evolution in Massive Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Modeling interactome: scale-free or geometric?
Bioinformatics
The degree distribution of the generalized duplication model
Theoretical Computer Science
Degree distribution of the FKP network model
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
The web as a graph: measurements, models, and methods
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
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Protein-protein interaction networks, particularly that of the yeast S. Cerevisiae, have recently been studied extensively. These networks seem to satisfy the small world property and their (1-hop) degree distribution seems to form a power law. More recently, a number of duplication based random graph models have been proposed with the aim of emulating the evolution of protein-protein interaction networks and satisfying these two graph theoretical properties. In this paper, we show that the proposed model of Pastor-Satorras et al. does not generate the power law degree distribution with exponential cutoff as claimed and the more restrictive model by Chung et al. cannot be interpreted unconditionally. It is possible to slightly modify these models to ensure that they generate a power law degree distribution. However, even after this modification, the more general k-hop degree distribution achieved by these models, for k 1, are very different from that of the yeast proteome network. We address this problem by introducing a new network growth model that takes into account the sequence similarity between pairs of proteins (as a binary relationship) as well as their interactions. The new model captures not only the k-hop degree distribution of the yeast protein interaction network for all k 0, but it also captures the 1-hop degree distribution of the sequence similarity network, which again seems to form a power law.