| Texto completo | |
| Autor(es): |
Guzman, Grover E. C.
;
Takahashi, Daniel Yasumasa
;
Fujita, Andre
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | JOURNAL OF COMPLEX NETWORKS; v. 13, n. 4, p. 18-pg., 2025-08-01. |
| Resumo | |
The spectral density of a graph is a key concept for quantitatively characterizing empirical networks. It has many applications, including community detection, graph signal processing, spectral embedding, network evolution, brain network analysis, and random graph modeling. The graph's spectral density is also crucial in developing statistical methods for graphs, such as model selection and comparative testing. Despite its broad applicability, a complete understanding of the relationship between a graph's spectral density and structure remains elusive. To advance our understanding of the relationship between graph spectra and their structure, we introduce a vertex-wise decomposition of the graph's spectral density, allowing us to determine each vertex's contribution to specific eigenvalues. We show that the decomposition of distinct isospectral graphs (graphs with identical spectra) can be distinguished by the vertex-wise graph spectra, showing that the proposed new quantities are finer invariants between isomorphic graphs. Finally, we apply these insights to analyze chemical molecules and identify genes associated with normal versus tumoral breast gene interaction networks. (AU) | |
| Processo FAPESP: | 13/07699-0 - Centro de Pesquisa, Inovação e Difusão em Neuromatemática - NeuroMat |
| Beneficiário: | Oswaldo Baffa Filho |
| Modalidade de apoio: | Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs |
| Processo FAPESP: | 24/03261-4 - Avanços na Estatística de Redes: extensões para HPC e hipergrafos. |
| Beneficiário: | André Fujita |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| Processo FAPESP: | 24/09195-3 - Um algoritmo de aproximação da distribuição espectral para séries temporais de redes |
| Beneficiário: | André Fujita |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| Processo FAPESP: | 23/18337-3 - Das células às interações sociais: uma abordagem integrativa baseada em IA para revelar os mecanismos subjacentes dos comportamentos e fenótipos humanos |
| Beneficiário: | André Fujita |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |