The analysis reveals the only exponential random graph model with independent dyads, implying significant findings for directed networks.
We show that the only exponential random graph model with n nodal parameters, dyads being independent, and the natural assumption of permutation-equivariant nodal parametrization is the {eta} model. In addition, we show that an exponential random graph model with similar assumptions but with fewer than n block parameters is the additive stochastic block model. We also provide similar results for directed networks
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Kayvan Sadeghi (2025) studied this question.
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