Complex networks as an emerging property of hierarchical preferential attachment

Complex networks as an emerging property of hierarchical preferential attachment Laurent H´ ebert-Dufresne,1, 2, ∗ Edward Laurence,1, ∗ Antoine Allard,3 Jean-Gabriel Young,1 and Louis J. Dub´ e1 1 D´ epartement de Physique, de G´ enie Physique, et... More

Complex networks as an emerging property of hierarchical preferential attachment Laurent H´ ebert-Dufresne,1, 2, ∗ Edward Laurence,1, ∗ Antoine Allard,3 Jean-Gabriel Young,1 and Louis J. Dub´ e1 1 D´ epartement de Physique, de G´ enie Physique, et d’Optique, Universit´ e Laval, Qu´ ebec (Qu´ ebec), Canada G1V 0A6 2 Santa Fe Institute, Santa Fe, NM, 87501 3 Departament de F´ ısica Fonamental, Universitat de Barcelona, Mart´ ı i Franqu` es 1, 08028 Barcelona, Spain 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 ent Less