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<p>Exponential random graph models (ERGMs) are flexible probability models allowing edge dependency. However, it is known that to a first-order approximation, many ERGMs behave like Erdös-Rényi random graphs, where edges are independent. In this paper, to distinguish ERGMs from Erdös-Rényi random graphs, we consider second-order approximations of ERGMs using two-stars and triangles. We prove that the second-order approximation indeed achieves second-order accuracy in the triangle-free case. The new approximation is formally obtained by the Hoeffding decomposition and rigorously justified using Stein’s method.</p>

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Second-order approximation of exponential random graph models

  • 期刊论文

  • 发表日期：

    2025年2月25日

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  • Wen-Yi Ding,
  • Xiao Fang

摘要

Exponential random graph models (ERGMs) are flexible probability models allowing edge dependency. However, it is known that to a first-order approximation, many ERGMs behave like Erdös-Rényi random graphs, where edges are independent. In this paper, to distinguish ERGMs from Erdös-Rényi random graphs, we consider second-order approximations of ERGMs using two-stars and triangles. We prove that the second-order approximation indeed achieves second-order accuracy in the triangle-free case. The new approximation is formally obtained by the Hoeffding decomposition and rigorously justified using Stein’s method.