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Umbral de detectabilidad en redes modulares ponderadas
Filippo Radicchi1, Filipi N Silva1, Alessandro Flammini1
1Indiana University, Center for Complex Networks and Systems Research, Luddy School of Informatics, Computing, and Engineering, Bloomington, Indiana 47408, USA.
Physical review. E
|February 20, 2026
Resumen
La detección de la estructura de la comunidad en las redes es posible hasta un cierto umbral de mezcla. Este umbral depende del grado de nodo y las distribuciones de peso de los bordes, con una mayor variabilidad en los pesos que dificultan la detección.
Área de la Ciencia:
- Ciencia de la red Ciencia de la red.
- Física estadística de las estadísticas.
- Análisis de datos Análisis de datos.
Sus antecedentes:
- Los algoritmos de detección comunitarios tienen como objetivo identificar grupos de nodos en las redes.
- El modelo ponderado de partición plantada es un punto de referencia estándar para evaluar los métodos de detección de la comunidad.
- La optimización de la modularidad espectral es una técnica común para la detección de comunidades.
Objetivo del estudio:
- Determinar las condiciones necesarias para la detección de particiones de la verdad fundamental en redes ponderadas.
- Para derivar analíticamente el nivel máximo de mezcla tolerado por la optimización de la modularidad espectral.
- Investigar el impacto de las diferentes distribuciones de peso de borde en la detectabilidad de la comunidad.
Principales métodos:
- Derivación analítica del umbral de detectabilidad.
- Análisis del modelo ponderado de partición plantada con dos comunidades de igual tamaño.
- Comparación de cinco distribuciones de peso de borde (Dirac, Poisson, exponencial, geométrico, firmado Bernoulli) bajo grados de nodo distribuidos por Poisson.
Principales resultados:
- El umbral de detectabilidad depende de los dos primeros momentos de grado de nodo y las distribuciones de peso de borde.
- Los pesos distribuidos de Dirac dan como resultado el umbral de detectabilidad más pequeño.
- Los pesos distribuidos exponencialmente aumentan el umbral por un factor de sqrt[2]; una mayor variabilidad de peso puede disminuir la detectabilidad.
Conclusiones:
- La variabilidad del peso del borde influye significativamente en la detectabilidad de la estructura de la comunidad.
- La incorporación de pesos de borde es perjudicial cuando no llevan información sobre la estructura de la comunidad.
- Los hallazgos proporcionan información sobre las limitaciones y el rendimiento de la optimización de la modularidad espectral en redes ponderadas.
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