Stopping explosion by penalising transmission to hubs in scale-free spatial random graphs

Understand

We study the spread of information in finite and infinite inhomogeneous spatial random graphs.

• We assume that each edge has a transmission cost that is a product of an i.i.d.
• random variable L and a penalty factor: edges between vertices of expected degrees w_1 and w_2 are penalised by a factor of (w_1w_2)^\mu for all \mu >0.
• We study this process for scale-free percolation, for (finite and infinite) Geometric Inhomogeneous Random Graphs, and for Hyperbolic Random Graphs, all with power law degree distributions with exponent \tau > 1.