In widely used models of biological contagion, interventions that randomly rewire edges (generally making them ‘longer’) accelerate spread. However, recent work has argued that highly clustered, rather than random, networks facilitate the spread of threshold-based contagions, such as those motivated by myopic best response for adoption of new innovations, norms and products in games of strategic complement. Here we show that minor modifications to this model reverse this result, thereby harmonizing qualitative facts about how network structure affects contagion. We analyse the rate of spread over circular lattices with rewired edges and show that having a small probability of adoption below the threshold probability is enough to ensure that random rewiring accelerates the spread of a noisy threshold-based contagion. This conclusion is verified in simulations of empirical networks and remains valid with partial but frequent enough rewiring and when adoption decisions are reversible but infrequently so, as well as in high-dimensional lattice structures.

在广泛使用的生物传染模型中，随机重新连接边缘（通常使它们“更长”）的干预措施加速了传播。然而，最近的研究表明，高度聚集的网络而不是随机的网络促进了基于阈值的传染的传播，例如在战略互补的游戏中采用新的创新、规范和产品的短视最佳反应所激发的网络。在这里，我们表明对该模型的微小修改可以扭转这一结果，从而协调有关网络结构如何影响传染的定性事实。我们分析了具有重新布线边缘的圆形格子上的传播速率，并表明采用低于阈值概率的小概率足以确保随机重新布线加速基于噪声阈值的传染的传播。这一结论在经验网络的模拟中得到了验证，并且在部分但足够频繁的重新布线以及采用决策是可逆的但不常见的情况下以及在高维晶格结构中仍然有效。