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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Stegehuis, Clara [1] ; Peron, Thomas [2]
Total Authors: 2
Affiliation:
[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
Total Affiliations: 2
Document type: Journal article
Source: JOURNAL OF PHYSICS-COMPLEXITY; v. 2, n. 4 DEC 2021.
Web of Science Citations: 0
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, 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)

FAPESP's process: 16/23827-6 - Analysis of epidemic and synchronization processes in complex networks
Grantee:Thomas Kaue Dal Maso Peron
Support Opportunities: Scholarships in Brazil - Post-Doctoral
FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
Grantee:Francisco Louzada Neto
Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC