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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.06223 |
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Table of Contents:
- Log-linear exponential random graph models are a specific class of statistical network models that have a log-linear representation. This class includes many stochastic blockmodel variants. In this paper, we focus on $β$-stochastic blockmodels, which combine the $β$-model with a stochastic blockmodel. Here, using recent results by Almendra-Hernández, De Loera, and Petrović, which describe a Markov basis for $β$-stochastic block model, we give a closed form formula for the maximum likelihood degree of a $β$-stochastic blockmodel. The maximum likelihood degree is the number of complex solutions to the likelihood equations. In the case of the $β$-stochastic blockmodel, the maximum likelihood degree factors into a product of Eulerian numbers.