  In the understanding of important edges in complex networks, the edges with
larger degree are naturally considered more important, and they will cause
greater destructiveness when attacked. However, through simulation analysis, we
conclude that this understanding needs to be based on certain preconditions. In
this article, the robustness of BA scale-free network and WS small-world
network is studied based on the edge-removal attack strategy considering the
edge load and cascading failure. Specific attack methods include: High Load
Edge-removal Attacks (HLEA) and Low Load Edge-removal Attacks (LLEA). The
simulation results show that the importance of edges is closely related to the
load parameter {\delta}. When 0<{\delta}<1, attacking the edge with smaller
degree will cause greater cascading failure. For this condition, the edge with
smaller degree is more important. When {\delta}=1, cascading failure is
basically independent of the edge degree. When {\delta}>1, attacking the edge
with larger degree will cause greater cascading failure. Therefore, the edge
with larger degree is more important for this condition.
