Please use this identifier to cite or link to this item:
|Title:||Degree distribution of large networks generated by the partial duplication model|
|Citation:||Li, S., Choi, K.P., Wu, T. (2013-03-11). Degree distribution of large networks generated by the partial duplication model. Theoretical Computer Science 476 : 94-108. ScholarBank@NUS Repository. https://doi.org/10.1016/j.tcs.2012.12.045|
|Abstract:||In this paper, we present a rigorous analysis on the limiting behavior of the degree distribution of the partial duplication model, a random network growth model in the duplication and divergence family that is popular in the study of biological networks. We show that for each non-negative integer k, the expected proportion of nodes of degree k approaches a limit as the network becomes large. This fills in a gap in previous studies. In addition, we prove that p=1/2, where p is the selection probability of the model, is the phase transition for the expected proportion of isolated nodes converging to 1, and hence answer a question raised in Bebek et al. [G. Bebek, P. Berenbrink, C. Cooper, T. Friedetzky, J. Nadeau, S.C. Sahinalp, The degree distribution of the generalized duplication model, Theoret. Comput. Sci. 369 (2006) 239-249]. We also obtain asymptotic bounds on the convergence rates of degree distribution. Since the observed networks typically do not contain isolated nodes, we study the subgraph consisting of all non-isolated nodes contained in the networks generated by the partial duplication model, and show that p=1/2 is again a phase transition for the limiting behavior of its degree distribution.|
|Source Title:||Theoretical Computer Science|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Jun 17, 2018
WEB OF SCIENCETM
checked on May 16, 2018
checked on Jun 8, 2018
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.