Network bypasses sustain complexity

Estrada, Ernesto; Gómez-Gardeñes, Jesús; Lacasa, Lucas
Proceedings of the National Academy of Sciences of the USA (PNAS) 120, e2305001120 (2023)

Real-world networks are neither regular nor random, a fact elegantly explained by
mechanisms such as the Watts–Strogatz or the Barabási-Albert models, among others.
Both mechanisms naturally create shortcuts and hubs, which while enhancing the
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.

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