  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.
