In the subcritical regime m = m_c(1-ε) with ε→0 and ε³n→∞, the largest component L1 satisfies L1 = (1+o_p(1)) * [2(α+2)/(α+1)] ε^{-2} log(ε³ n) for fixed α>0 (and analogous limits when α(n)→a).
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Defines the H_α family of balance indices for phylogenetic networks, establishes structural properties including a grafting property, and analyzes minima, maxima, and distributions under random models such as Yule and PDA.
PageRank on undirected multi-type PAMs satisfies the power-law hypothesis with color-dependent exponents for finite colors under certain initial color distributions and attractiveness functions.
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Sharp Asymptotics for the Largest Component in the Subcritical Regime of Preferential Attachment Without Vertex Growth
In the subcritical regime m = m_c(1-ε) with ε→0 and ε³n→∞, the largest component L1 satisfies L1 = (1+o_p(1)) * [2(α+2)/(α+1)] ε^{-2} log(ε³ n) for fixed α>0 (and analogous limits when α(n)→a).
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A parameterized family of balance indices for phylogenetic networks
Defines the H_α family of balance indices for phylogenetic networks, establishes structural properties including a grafting property, and analyzes minima, maxima, and distributions under random models such as Yule and PDA.
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Power-law hypothesis and (un)fairness of PageRank on undirected multi-type PAMs
PageRank on undirected multi-type PAMs satisfies the power-law hypothesis with color-dependent exponents for finite colors under certain initial color distributions and attractiveness functions.