Exploring the step function distribution of the threshold fraction of adopted neighbors versus minimum fraction of nodes as initial adopters to assess the cascade blocking intra-cluster density of complex real-world networks

Applied Network Science

Table 1 Execution of the Jump Zone Analyzer binary search algorithm on the jump zone for the karate club network

It #	LI	RI	\|RI—LI\|, ≥ 0.001, ?	MI	\(f_{IA}^{\min ,LI}\)	\(f_{IA}^{\min ,RI}\)	\(f_{IA}^{\min ,MI}\)	\(\left( \begin{gathered} \|f_{IA}^{\min ,MI} - f_{IA}^{\min ,LI} \| \le \hfill \\ \|f_{IA}^{\min ,RI} - f_{IA}^{\min ,MI} \| \hfill \\ \end{gathered} \right)\), ?	Change
1	0.30	0.35	0.05, Yes	0.325	0.0294	0.4118	0.0294	0 ≤ 0.3824, Yes	LI = MI
2	0.325	0.35	0.025, Yes	0.3375	0.0294	0.4118	0.3823	0.3529 ≤ 0.0295, No	RI = MI
3	0.325	0.3375	0.0125, Yes	0.3313	0.0294	0.3823	0.0294	0 ≤ 0.3529, Yes	LI = MI
4	0.3313	0.3375	0.0062, Yes	0.3344	0.0294	0.3823	0.3823	0.3529 ≤ 0, No	RI = MI
5	0.3313	0.3344	0.0031, Yes	0.3329	0.0294	0.3823	0.0294	0 ≤ 0.3529, Yes	LI = MI
6	0.3329	0.3344	0.0015, Yes	0.3337	0.0294	0.3823	0.3529	0.3235 ≤ 0.0294, No	RI = MI
7	0.3329	0.3337	0.0008, No	STOP!! q_step = 0.3329; \(\underline{{f_{IA}^{\min } }}\) = 0.0294; \(\overline{{f_{IA}^{\min } }}\) = 0.3823