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In actual networks, the distance between nodes has an effect on load flow. Nodes closer to a node are more attractive, as if there is some kind of gravity between the nodes. For example, vehicles and people usually prefer to a close place in the traffic network. Does the distance between nodes affect the load distribution of the network, and how does this “gravity” affect the cascading dynamics? To this end, we propose a new cascading model under the global dynamics of the load distribution, which take the gravitational effect between nodes into account and have three controllable parameters, the weight parameter
α
, the gravity parameter
γ
, the ability parameter
β
. In several actual traffic networks, classical BA scale-free and WS small-world networks, we find that increasing the value of
α
or
γ
in the network will expand the cascading failures’ scale and make the robustness of the network decrease. And the abnormal phenomenon that the robustness of the network decreases with the increase of the value of
β
also raises our concern. We have observed the above phenomena in the power grid too. Through deductive reasoning and testing on small-scale networks, we analyzed the cause of this abnormal dynamics that the negative correlation between the gravity parameter and the robustness of the network may be caused by changing the approximate reachable region of the load flow. The existence of the ability paradox is due to the increasing capacity to resurrect of the key edges in the annular structure and causes partially paralysis.