Critical stretching in spatial networks

Prof. Shlomo Havlin and his team in a new article.

Physical situations of experimental relevance often involve spatially embedded systems, whose range of interactions is constrained by some wiring-cost function. Motivated by recent observations reported in transport networks and in mammal connectomes, we have studied a spatial network model built on an underlying grid of points, having homogeneous connectivities and a characteristic scale ζ of link-lengths. We have found that, while away from the percolation threshold a structural crossover from a random, Erdos–Rényi structure to a d-dimensional lattice occurs at the characteristic length ζ, close to criticality it stretches in space until a universal length scale ξ*. This means that mean-field regimes are stretched not only in space but furthermore in time when the underlying structure is close to its percolation threshold, as we demonstrated in epidemic processes. Besides of theoretical interest, these results yield significant implications on the spatio-temporal scales of real-world phenomena like neural activation or traffic flows.

The article published at Physical Review Letters Journal.