Network bypasses sustain complexity

TL;DR

This paper explores how complex networks, like the human brain, develop alternative routes called bypasses that improve navigation and resilience, explaining their ubiquity and functional advantages.

Contribution

It introduces a mathematical theory for the emergence of network bypasses and applies it to real-world networks, revealing their role in sustaining complexity.

Findings

Networks generate topologically longer but navigationally easier bypasses.

Real-world networks, especially the human brain, have high levels of network bypasses.

Bypasses enhance network navigability and resilience.

Abstract

Real-world networks are neither regular nor random, a fact elegantly explained by mechanisms such as the Watts-Strogatz or the Barabasi-Albert models, among others. Both mechanisms naturally create shortcuts and hubs, which while enhancing network's connectivity, also might yield several undesired navigational effects: they tend to be overused during geodesic navigational processes -- making the networks fragile -- and provide suboptimal routes for diffusive-like navigation. Why, then, networks with complex topologies are ubiquitous? Here we unveil that these models also entropically generate network bypasses: alternative routes to shortest paths which are topologically longer but easier to navigate. We develop a mathematical theory that elucidates the emergence and consolidation of network bypasses and measure their navigability gain. We apply our theory to a wide range of real-world networks and find that they sustain complexity by different amounts of network bypasses. At the top of this complexity ranking we found the human brain, which points out the importance of these results to understand the plasticity of complex systems.