2021/04/30 by Clara Stegehuis, Stegehuis, Clara, Thomas Peron +1
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #FOS: Physical sciences #Opinion Dynamics and Social Influence #Physics and Society (physics.soc-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2104.14776
openalex publication_date 2021/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate the effect of local structures on network\nprocesses. We investigate a random graph model that incorporates local clique\nstructures to deviate from the locally tree-like behavior of most standard\nrandom graph models. For the process of bond percolation, we derive analytical\napproximations for large outbreaks and the critical percolation value.\nInterestingly, these derivations show that when the average degree of a vertex\nis large, the influence of the deviations from the locally tree-like structure\nis small. Our simulations show that this insensitivity to local clique\nstructures often already kicks in for networks with average degrees as low as\n6. Furthermore, we show that the different behavior of bond percolation on\nclustered networks compared to tree-like networks that was found in previous\nworks can be almost completely attributed to differences in degree sequences\nrather than differences in clustering structures. We finally show that these\nresults also extend to completely different types of dynamics, by deriving\nsimilar conclusions and simulations for the Kuramoto model on the same types of\nclustered and non-clustered networks.\n