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).
Time evolution of dense multigraph limits under edge-conservative pref- erential attachment dynamics.Random Structures & Algorithms, 41(3):365–390, 2012
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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).