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Some asymptotic properties of duplication graphs | Alpan Raval
; | Date: |
30 Jul 2003 | Subject: | Statistical Mechanics; Molecular Networks | cond-mat.stat-mech q-bio.MN | Abstract: | Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are studied: pure duplication growth, and two two-parameter models in which duplication forms one element of the growth dynamics. A power-law degree distribution is found to emerge in all three models. However, the parameter space of the latter two models is characterized by a range of parameter values for which duplication is the predominant mechanism of graph growth. For parameter values that lie in this ``duplication-dominated’’ regime, it is shown that the degree distribution either approaches zero asymptotically, or approaches a non-zero power-law degree distribution very slowly. In either case, the approach to the true asymptotic degree distribution is characterized by a dependence of the scaling exponent on properties of the initial degree distribution. It is therefore conjectured that duplication-dominated, scale-free networks may contain identifiable remnants of their early structure. This feature is inherited from the idealized model of pure duplication growth, for which the exact finite-size degree distribution is found and its asymptotic properties studied. | Source: | arXiv, cond-mat/0307717 | Other source: | [GID 798531] pmid14754281 | Services: | Forum | Review | PDF | Favorites |
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