Abstract
Complex networks emerging in natural and human-made systems tend to assume small-world structure. Is there a common mechanism underlying their self-organisation? Our computational simulations show that network diffusion (traffic flow or information transfer) steers network evolution towards emergence of complex network structures. The emergence is effectuated through adaptive rewiring: progressive adaptation of structure to use, creating short-cuts where network diffusion is intensive while annihilating underused connections. With adaptive rewiring as the engine of universal small-worldness, overall diffusion rate tunes the systems’ adaptation, biasing local or global connectivity patterns. Whereas the former leads to modularity, the latter provides a preferential attachment regime. As the latter sets in, the resulting small-world structures undergo a critical shift from modular (decentralised) to centralised ones. At the transition point, network structure is hierarchical, balancing modularity and centrality - a characteristic feature found in, for instance, the human brain.
Highlights
Complex network structures emerge in protein[1] and ecological networks[2], social networks[3], the mammalian brain[4,5,6], and the World Wide Web[7]
This study generalises previous work on adaptive rewiring[10,11,12,13,14]. While these studies have shown that small–world network (SWN) robustly emerge through rewiring according to the ongoing dynamics on the network, the claim to universality has been frustrated by need to explicitly specify the dynamics
We proposed a mechanism of network self-organisation that relies on ongoing network diffusion; over time, the network is rewired adaptively, rendering it conform to the patterns of network diffusion
Summary
Complex network structures emerge in protein[1] and ecological networks[2], social networks[3], the mammalian brain[4,5,6], and the World Wide Web[7] All these self-organising systems tend to assume small–world network (SWN) structure. Thereby the network largely maintains the regular clustering, while the rewiring creates shortcuts that enhance the networks connectedness As it shows how these properties are reconciled in a very basic manner, the Watts-Strogatz rewiring algorithm has a justifiable claim to universality. In contrast with the random rewirings in the Watts-Strogatz algorithm, here, they have the function of perturbing possible equilibrium network states, akin to the Boltzmann machine[16] In this sense, the perturbed system can be regarded as an open system according to the criteria of thermodynamics
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