| Full text | |
| Author(s): |
Pham, Tuan Minh
;
Peron, Thomas
;
Metz, Fernando L.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | PHYSICAL REVIEW E; v. 110, n. 5, p. 13-pg., 2024-11-19. |
| Abstract | |
We derive exact equations for the spectral density of sparse networks with an arbitrary distribution of the number of single edges and triangles per node. These equations enable a systematic investigation of the effects of clustering on the spectral properties of the network adjacency matrix. In the case of heterogeneous networks, we demonstrate that the spectral density becomes more symmetric as the fluctuations in the triangle-degree sequence increase. This phenomenon is explained by the small clustering coefficient of networks with a large variance of the triangle-degree distribution. In the homogeneous case of regular clustered networks, we find that both perturbative and nonperturbative approximations fail to predict the spectral density in the high-connectivity limit. This suggests that traditional large-degree approximations may be ineffective in studying the spectral properties of networks with more complex motifs. Our theoretical results are fully confirmed by numerical diagonalizations of finite adjacency matrices. (AU) | |
| FAPESP's process: | 23/07481-6 - Synchronization in networks: applications in neuroscience |
| Grantee: | Thomas Kaue Dal Maso Peron |
| Support Opportunities: | Regular Research Grants |
| 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 |