Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/103118
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dc.titleDegree distribution of large networks generated by the partial duplication model
dc.contributor.authorLi, S.
dc.contributor.authorChoi, K.P.
dc.contributor.authorWu, T.
dc.date.accessioned2014-10-28T02:33:33Z
dc.date.available2014-10-28T02:33:33Z
dc.date.issued2013-03-11
dc.identifier.citationLi, 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.
dc.identifier.issn03043975
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/103118
dc.description.abstractIn 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.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1016/j.tcs.2012.12.045
dc.sourceScopus
dc.subjectComputational proteomics
dc.subjectDegree distribution
dc.subjectLimiting behavior
dc.subjectPower law
dc.subjectRandom graph
dc.typeArticle
dc.contributor.departmentSTATISTICS & APPLIED PROBABILITY
dc.contributor.departmentMATHEMATICS
dc.description.sourcetitleTheoretical Computer Science
dc.description.volume476
dc.description.page94-108
dc.description.codenTCSCD
dc.identifier.isiut000315553500008
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