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Real complex systems are not rigidly structured; no clear rules or blueprintsexist for their construction. Yet, amidst their apparent randomness, complexstructural properties universally emerge. We propose that an important class ofcomplex systems can be modeled as an organization of many embedded levels(potentially infinite in number), all of them following the same universalgrowth principle known as preferential attachment. We give examples of suchhierarchy in real systems, for instance in the pyramid of production entitiesof the film industry. More importantly, we show how real complex networks canbe interpreted as a projection of our model, from which their scaleindependence, their clustering, their hierarchy, their fractality and theirnavigability naturally emerge. Our results suggest that complex networks,viewed as growing systems, can be quite simple, and that the apparentcomplexity of their structure is largely a reflection of their unobservedhierarchical nature.

Complex networks as an emerging property of hierarchical preferential attachment