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Navigability, an ability to find a logarithmically short path betweenelements using only local information, is one of the most fascinatingproperties of real-life networks. However, the exact mechanism responsible forthe formation of navigation properties remained unknown. We show thatnavigability can be achieved by using only two ingredients present in themajority of networks: network growth and local homophily, giving a persuasiveanswer how the navigation appears in real-life networks. A very simplealgorithm produces hierarchical self-similar optimally wired navigable smallworld networks with exponential degree distribution by using only localinformation. Adding preferential attachment produces a scale-free network whichhas shorter greedy paths, but worse (power law) scaling of the informationextraction locality (algorithmic complexity of a search). Introducingsaturation of the preferential attachment leads to truncated scale-free degreedistribution that offers a good tradeoff between these parameters and can beuseful for practical applications. Several features of the model are observedin real-life networks, in particular in the brain neural networks, supportingthe earlier suggestions that they are navigable.

Growing homophilic networks are natural navigable small worlds