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.
Highlights
Large scale networks are ubiquitous in many domains of science and technology
Our study shows that the Growing Homophilic (GH) networks have high level features that are found in the functional brain networks, indicating that the GH mechanism is not suppressed and plays a significant role in brain network formation, supporting the earlier suggestions that the brain networks are naturally navigable
Using simulations and theoretical studies we have demonstrated that two ingredients that are present in the majority of networks, namely network growth and local homophily, are sufficient to produce a navigable small world network, giving a simple and persuasive answer how the navigation feature appears in real-life networks
Summary
Large scale networks are ubiquitous in many domains of science and technology. They influence numerous aspects of daily human life, and their importance is rising with the advances in the information technology. Even human’s ability to think is governed by a large-scale brain network containing more than 100 billion neurons[1]. One of the most fascinating features found in the real-life networks is the navigability, an ability to find a logarithmically short path between two arbitrary nodes using only local information, without global knowledge of the network. Participants forwarded the letter to an acquaintance that was more likely to know the target. As a result about 20% of the letters arrived to the target on the average in less than
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
