Critical stretching of mean-field regimes in spatial networks

Abstract

We study a spatial network model with exponentially distributed link-lengths on an underlying grid of points, undergoing a structural crossover from a random, Erdős--Rényi graph to a $2D$ lattice at the characteristic interaction range $\zeta$. We find that, whilst far from the percolation threshold the random part of the incipient cluster scales linearly with $\zeta$, close to criticality it extends in space until the universal length scale ${\zeta }^{3/2}$ before crossing over to the spatial one. We demonstrate this {\em critical stretching} phenomenon in percolation and in dynamical processes, and we discuss its implications to real-world phenomena, such as neural activation, traffic flows or epidemic spreading.

Manuscript with supplementary information attached

References in corpus (5)

• Critical phenomena in complex networks
• Geographical dispersal of mobile communication networks
• Small vulnerable sets determine large network cascades in power grids
• Structural properties of spatially embedded networks
• Transitions in spatial networks

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