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FIELD
Computational Sciences
DATE
Mar 11 (Mon), 2024
TIME
10:00 ~ 12:00
PLACE
7323
SPEAKER
Yang, Seong-Gyu
HOST
Yang, Seong-Gyu
INSTITUTE
계산과학부
TITLE
[GS_C_DS] Random graph ensembles may give different significance of structural correlations
ABSTRACT
Numerous empirical networks display inherent structural correlations, which may stem from the network formation mechanisms. Therefore, it is crucial to discern whether these correlations arise from random mixing by chance or not. In this sense, null models play a crucial role in assessing the significance of the correlations. In this study, we compare two null models which are arbitrarily chosen; one is the exponential random graph (ERG) model, and the other is degree-preserving edge rewiring Markov Chain Monte Carlo (MCMC) method. In the language of statistical physics, ERG corresponds to the canonical ensemble with constraints in expectation values and the MCMC does to the microcanonical ensemble with stricter constraints in values themselves. In the limit of large sparse network, we analytically derive the mean and width of degree assortativity distribution in ERG ensemble and corroborate the results through numerical simulations. Our analytic findings provide systematic understanding on how the degree assortativity behaves with system size. While both ensembles exhibit similar behavior in system size, they differ in their prefactors. Specifically, while the degree assortativity distributions align across two different ensembles for scale-free networks, the exponential random graph ensemble demonstrates broader distributions for Erd{\"o}s-R{\'e}nyi graphs. These results indirectly suggest the ensemble nonequivalence in homogeneous networks, underscoring the importance of carefully selecting null models, particularly in homogeneous networks.
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