Speed vs Resilience in Contagion

We highlight a trade-off between speed (the rate at which behaviours propagate in the population) and resilience (the measure of initial adopters required for spreading) in models of threshold contagion: contagion is faster in networks where it is harder to initiate contagion. We derive various orderings over networks under which this trade-off is stark. While this trade-off holds between pairs of networks for possibly different contagion thresholds, we also outline conditions under which, for a given contagion threshold, one network is both less resilient and propagates behaviours more quickly; this highlights the role of intermediate links as bulwarks against contagion