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

Autor(es)

Stegehuis, Clara ^[1] ; Peron, Thomas ^[2]

Afiliação do(s) autor(es)

^[1] Twente Univ, Dept Elect Engn Math & Comp Sci, Enschede - Netherlands

^[2] Univ Sao Paulo, Inst Math & Comp Sci, BR-13566590 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF PHYSICS-COMPLEXITY; v. 2, n. 4 DEC 2021.
• Citações Web of Science: 0

Resumo

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, we 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. (AU)

• Processo FAPESP: 16/23827-6 - Análise de processos epidêmicos e de sincronização em redes complexas
• Beneficiário: Thomas Kaue Dal Maso Peron
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs