title: Complex networks as an emerging property of hierarchical preferential attachment.
abstract: Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of complex systems can be modeled as an organization of many embedded levels (potentially infinite in number), all of them following the same universal growth principle known as preferential attachment. We give examples of such hierarchy in real systems, for instance, in the pyramid of production entities of the film industry. More importantly, we show how real complex networks can be interpreted as a projection of our model, from which their scale independence, their clustering, their hierarchy, their fractality, and their navigability naturally emerge. Our results suggest that complex networks, viewed as growing systems, can be quite simple, and that the apparent complexity of their structure is largely a reflection of their unobserved hierarchical nature.
authors.affiliation: Département de Physique, de Génie Physique, et d'Optique, Université Laval, Québec (Québec), Canada G1V 0A6.|Santa Fe Institute, Santa Fe, New Mexico 87501, USA.
authors.forename: Laurent
authors.initials: L
authors.lastname: Hébert-Dufresne
authors.affiliation: Département de Physique, de Génie Physique, et d'Optique, Université Laval, Québec (Québec), Canada G1V 0A6.
authors.forename: Edward
authors.initials: E
authors.lastname: Laurence
authors.affiliation: Departament de Física Fonamental, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain.
authors.forename: Antoine
authors.initials: A
authors.lastname: Allard
authors.affiliation: Département de Physique, de Génie Physique, et d'Optique, Université Laval, Québec (Québec), Canada G1V 0A6.
authors.forename: Jean-Gabriel
authors.initials: JG
authors.lastname: Young
authors.affiliation: Département de Physique, de Génie Physique, et d'Optique, Université Laval, Québec (Québec), Canada G1V 0A6.
authors.forename: Louis J
authors.initials: LJ
authors.lastname: Dubé
mesh_terms: D000465:Algorithms; D016000:Cluster Analysis; D017709:Fractals; D008962:Models, Theoretical