We first propose a binary search algorithm to determine the minimum fraction of nodes in a network to be used as initial adopters (\(f_{IA}^{\min }\)) for a particular threshold fraction (q) of adopted neighbors (related to the cascade capacity of the network) leading to a complete information cascade. We observe the q versus \(f_{IA}^{\min }\) distribution for several complex real-world networks to exhibit a step function pattern wherein there is an abrupt increase in \(f_{IA}^{\min }\) beyond a certain value of q (q_step); the \(f_{IA}^{\min }\) values at q_step and the next measurable value of q are represented as \(\underline{{f_{IA}^{\min } }}\) and \(\overline{{f_{IA}^{\min } }}\) respectively. The difference \(\overline{{f_{IA}^{\min } }} - \underline{{f_{IA}^{\min } }}\) is observed to be significantly high (a median of 0.44 for a suite of 40 real-world networks studied in this paper) such that we claim the 1 − q_step value (we propose to refer 1 − q_step as the Cascade Blocking Index, CBI) for a network could be perceived as a measure of the intra-cluster density of the blocking cluster of the network that cannot be penetrated without including an appreciable number of nodes from the cluster to the set of initial adopters (justifying a relatively larger \(\overline{{f_{IA}^{\min } }}\) value).

我们首先提出一种二分查找算法，以确定被采用邻居的特定阈值分数（q）的网络中用作初始采用者的节点的最小分数（\（f_ {IA} ^ {\ min} \））。与网络的级联容量有关）导致完整的信息级联。我们观察到几个复杂的现实世界网络的q与\（f_ {IA} ^ {\ min} \）分布，表现出阶跃函数模式，其中\（f_ {IA} ^ {\ min}突然增加\）超出q的某个值（q_步）；q_步的\（f_ {IA} ^ {\ min} \）值和下一个可测量的值q表示为\（\下划线{{F_ {IA} ^ {\分钟}}} \）和\（\划线{{F_ {IA} {\分钟}} ^} \）分别。观察到差异\（\ overline {{f_ {IA} ^ {\ min}}}-\ underline {{f_ {IA} ^ {\ min}}} \）很高（对于本文研究的40个真实世界网络的集合）使得我们要求1 −  q_步长值（我们建议参考1 −  q_步长（例如，网络的级联阻塞指数，CBI）可以看作是网络阻塞群集的群集内密度的度量，如果不包括从群集到初始采用者集合的可观数量的节点，则无法穿透该阻塞群集（调整相对较大的\（\ overline {{f_ {IA} ^ {\\ min}}} \）值）。