Sudden emergence of a giant k-core in a random graph
Journal of Combinatorial Theory Series B
First to market is not everything: an analysis of preferential attachment with fitness
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A Course on the Web Graph
A geometric model for on-line social networks
WOSN'10 Proceedings of the 3rd conference on Online social networks
Rank-based models of network structure and the discovery of content
WAW'11 Proceedings of the 8th international conference on Algorithms and models for the web graph
| Hi-index | 5.23 |
We introduce a new class of random graph models for complex real-world networks, based on the protean graph model by Luczak and Pralat. Our generalized protean graph models have two distinguishing features. First, they are not growth models, but instead are based on the assumption that a ''steady state'' of large but finite size has been reached. Second, the models assume that the vertices are ranked according to a given ranking scheme, and the rank of a vertex determines the probability that that vertex receives a link in a given time step. Precisely, the link probability is proportional to the rank raised to the power -@a, where the attachment strength @a is a tunable parameter. We show that the model leads to a power law degree distribution with exponent 1+1/@a for ranking schemes based on a given prestige label, or on the degree of a vertex. We also study a scheme where each vertex receives an initial rank chosen randomly according to a biased distribution. In this case, the degree distribution depends on the distribution of the initial rank. For one particular choice of parameters we obtain a power law with an exponent that depends both on @a and on a parameter determining the initial rank distribution.