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).
Connected components in random graphs with given expected degree sequences.Annals of Combinatorics, 6(2):125–145, 2002
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A self-consistent framework with generalized local order parameters is derived for the Kuramoto model with dyadic and triadic interactions on hypergraphs, showing bistability onset depends on eigenvector correlations between dyadic and triadic structures.
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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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Self-consistent analysis of the Kuramoto model with higher-order interactions
A self-consistent framework with generalized local order parameters is derived for the Kuramoto model with dyadic and triadic interactions on hypergraphs, showing bistability onset depends on eigenvector correlations between dyadic and triadic structures.