Previous studies on the invulnerability of scale-free networks under edge attacks supported the conclusion that scale-free networks would be fragile under selective attacks. However, these studies are based on qualitative methods with obscure definitions on the robustness. This paper therefore employs a quantitative method to analyze the invulnerability of the scale-free networks, and uses four scale-free networks as the experimental group and four random networks as the control group. The experimental results show that some scale-free networks are robust under selective edge attacks, different to previous studies. Thus, this paper analyzes the difference between the experimental results and previous studies, and suggests reasonable explanations.