title: Growing Homophilic Networks Are Natural Navigable Small Worlds.
abstract: Navigability, an ability to find a logarithmically short path between elements using only local information, is one of the most fascinating properties of real-life networks. However, the exact mechanism responsible for the formation of navigation properties remained unknown. We show that navigability can be achieved by using only two ingredients present in the majority of networks: network growth and local homophily, giving a persuasive answer how the navigation appears in real-life networks. A very simple algorithm produces hierarchical self-similar optimally wired navigable small world networks with exponential degree distribution by using only local information. Adding preferential attachment produces a scale-free network which has shorter greedy paths, but worse (power law) scaling of the information extraction locality (algorithmic complexity of a search). Introducing saturation of the preferential attachment leads to truncated scale-free degree distribution that offers a good tradeoff between these parameters and can be useful for practical applications. Several features of the model are observed in real-life networks, in particular in the brain neural networks, supporting the earlier suggestions that they are navigable.
authors.affiliation: Federal state budgetary institution of science, Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov Street, 603950, Nizhny Novgorod, Russia.
authors.forename: Yury A
authors.initials: YA
authors.lastname: Malkov
authors.affiliation: Laboratory of Algorithms and Technologies for Network Analysis, National Research University Higher School of Economics, Nizhny Novgorod, Russia.
authors.forename: Alexander
authors.initials: A
authors.lastname: Ponomarenko
mesh_terms: D000465:Algorithms; D001921:Brain / Q000502:physiology; D008954:Models, Biological; D008962:Models, Theoretical; D016571:Neural Networks, Computer