The degree sequence of a scale-free random graph process
Random Structures & 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
On the bias of traceroute sampling: or, power-law degree distributions in regular graphs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Graph mining: Laws, generators, and algorithms
ACM Computing Surveys (CSUR)
The degree sequences and spectra of scale-free random graphs
Random Structures & Algorithms
The degree distribution of the generalized duplication model
Theoretical Computer Science
On certain properties of random apollonian networks
WAW'12 Proceedings of the 9th international conference on Algorithms and Models for the Web Graph
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A power law degree distribution is established for a graph evolution model based on the graph class of k-trees. This k-tree-based graph process can be viewed as an idealized model that captures some characteristics of the preferential attachment and copying mechanisms that existing evolving graph processes fail to model due to technical obstacles. The result also serves as a further cautionary note reinforcing the point of view that a power law degree distribution should not be regarded as the only important characteristic of a complex network, as has been previously argued [D. Achlioptas, A. Clauset, D. Kempe, C. Moore, On the bias of traceroute sampling, or power-law degree distribution in regular graphs, in: Proceedings of the 37th ACM Symposium on Theory of Computing, STOC'05, 2005, pp. 694-703; L. Li, D. Alderson, J. Doyle, W. Willinger, Towards a theory of scale-free graphs: Definition, properties, and implications, Internet Mathematics 2 (4) (2005) 431-523; M. Mitzenmacher, The future of power law research, Internet Mathematics, 2 (4) (2005) 525-534].