Network processes on clique-networks with high average degree: The limited effect of higher-order structure

Clara Stegehuis*, Thomas Peron

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
24 Downloads (Pure)

Abstract

In this paper, we investigate the effect of local structures on network processes. We investigate a random graph model that incorporates local clique structures, and thus deviates from the locally tree-like behavior of most standard random graph models. For the process of bond percolation, w derive analytical approximations for large percolation probabilities and the critical percolation value. Interestingly, these derivations show that when the average degree of a vertex is large, the influence of the deviations from the locally tree-like structure is small. In our simulations, this insensitivity to local clique structures often already kicks in for networks with average degrees as low as 6. Furthermore, we show that the different behavior of bond percolation on clustered networks compared to tree-like networks that was found in previous works can be almost completely attributed to differences in degree sequences rather than differences in clustering structures. We finally show that these results also extend to completely different types of dynamics by deriving similar conclusions and simulations for the Kuramoto model on the same types of clustered and non-clustered networks.

Original languageEnglish
Article number045011
JournalJournal of Physics: Complexity
Volume2
Issue number4
DOIs
Publication statusPublished - Dec 2021

Keywords

  • Configuration model
  • Network processes
  • Percolation
  • Random graphs
  • Synchronization
  • Transitivity
  • UT-Gold-D

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