Minimal contagious sets: Degree distributional bounds
研究了网络中最少需要多少人采纳创新才能引发全体采纳，并给出了仅依赖度分布的上界和下界，发现除极端网络外，必须种子化大量人口才能实现传染。
Agents in a network adopt an innovation if a certain fraction of their neighbors has already done so. We study the minimal contagious set size required for a successful innovation adoption by the entire population, and provide upper and lower bounds on it. Since detailed information about the network structure is often unavailable, we study bounds that depend only on the degree distribution of the network – a simple statistic of the network topology. Moreover, as our bounds are robust to small changes in the degree distribution, they also apply to large networks for which the degree distribution can only be approximated. Applying our bounds to growing networks shows that the minimal contagious set size is linear in the number of nodes. Consequently, for outside of knife-edge cases (such as the star-shaped network), contagion cannot be achieved without seeding a significant fraction of the population. This finding highlights the resilience of networks and demonstrates a high penetration cost in the corresponding markets.