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For the inhomogeneous random graph with kernel of preferential attachment type and degree distribution with power-law exponent \(\tau \in (2,3)\) we study the decay of the size of the giant component when the edge density approaches zero. It turns out that the giant component is significantly smaller than for the inhomogeneous random graph with a kernel of rank one.

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The Size of the Giant in Inhomogeneous Random Graphs of Preferential Attachment Type

  • 会议论文

  • 发表日期：

    2025年

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  • Peter Mörters,
  • Lucas Schätze

摘要

For the inhomogeneous random graph with kernel of preferential attachment type and degree distribution with power-law exponent \(\tau \in (2,3)\) we study the decay of the size of the giant component when the edge density approaches zero. It turns out that the giant component is significantly smaller than for the inhomogeneous random graph with a kernel of rank one.