Fig. 2

a (Log scale) Load as a function of r,  the distance from the center, for a \({\mathbb {H}}_{3,7}\) grid with radius 8, i.e. with \(N=11{,}173.\) Demand is only broadcast from the center, uniformly to all other nodes. The plot of \(\ln [\Lambda (r) - \Lambda (\infty )]\) is a linear function of r,  implying exponential decay of the load as a function of r,  towards its asymptotic value at \(r\rightarrow \infty .\) b Load at the center as a function of the radius of the \({\mathbb {H}}_{3,7}\) grid. The load is a linear function of the radius, i.e. a linear function of \(\ln N\) for large N.