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Auto-similaridad de las redes complejas
Chaoming Song1, Shlomo Havlin, Hernán A Makse
1Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA.
Nature
|January 28, 2005
Resumen
Las redes complejas exhiben patrones de autorrepetición en todas las escalas, desafiando las suposiciones anteriores. Este hallazgo revela un exponente auto-similar finito, explicando su naturaleza libre de escala y sugiriendo dinámicas universales de auto-organización.
Área de la Ciencia:
- Ciencia de la red Ciencia de la red Ciencia de la red.
- Física Estadística Física de las estadísticas.
- Sistemas complejos de sistemas complejos.
Sus antecedentes:
- Las redes complejas, incluyendo Internet y los sistemas biológicos, son a menudo libres de escala, exhibiendo distribuciones de grados de ley de poder.
- Las teorías existentes sugieren que las redes complejas carecen de invariancia bajo transformaciones de escala de longitud debido a sus propiedades de mundo pequeño.
- Esta percepción de falta de auto-similaridad contradice el comportamiento esperado de las estructuras fractales o auto-similares.
Objetivo del estudio:
- Investigar la invarianza de escala y la autosimilaridad de las redes complejas del mundo real.
- Desafiar la opinión predominante de que las redes complejas no son auto-similares en diferentes escalas de longitud.
- Identificar las propiedades fundamentales que rigen la estructura y organización de redes complejas.
Principales métodos:
- Análisis de diversas redes complejas del mundo real.
- Aplicación de un procedimiento de renormalización que implica el grueso de grano en cajas de diferentes tamaños.
- Cuantificación de la relación entre el número de cajas y el tamaño de la caja para determinar los exponentes de escala.
Principales resultados:
- Contrariamente a las creencias anteriores, las redes complejas demuestran patrones de autorrepetición en todas las escalas de longitud.
- Se identificó una relación de poder-ley entre el número de cajas requeridas para cubrir una red y el tamaño de estas cajas.
- Se determinó un exponente auto-similar finito para estas redes complejas.
Conclusiones:
- Las redes complejas exhiben una autosimilaridad inherente, caracterizada por un exponente de escalado finito.
- La auto-similaridad identificada proporciona una explicación fundamental para las propiedades observadas sin escala de muchas redes del mundo real.
- Estos hallazgos sugieren un mecanismo de autoorganización subyacente común que impulsa la formación de estructuras de red complejas.
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