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 \(\alpha \), the gravity parameter \(\gamma \), the ability parameter \(\beta \). In several actual traffic networks, classical BA scale-free and WS small-world networks, we find that increasing the value of \(\alpha \) or \(\gamma \) 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 \(\beta \) 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.

在实际网络中，节点之间的距离对潮流有影响。离节点越近的节点越有吸引力，就好像节点之间存在某种引力一样。例如，车辆和人在交通网络中通常更喜欢靠近的地方。节点之间的距离是否会影响网络的负载分布，这种“重力”如何影响级联动力学？为此，我们提出了一种新的载荷分布全局动力学下的级联模型，该模型考虑了节点之间的重力效应，具有三个可控参数，权重参数\(\alpha \)、重力参数\(\ gamma \)，能力参数\(\beta \). 在几个实际的交通网络，经典的 BA 无标度网络和 WS 小世界网络中，我们发现增加网络中\(\alpha \)或\(\gamma \)的值会扩大级联故障的规模，使网络的鲁棒性下降。而网络的鲁棒性随着\(\beta\)值的增加而降低的异常现象也引起了我们的关注。我们在电网中也观察到了上述现象。通过对小规模网络的演绎推理和测试，我们分析了这种异常动力学的原因，即重力参数与网络鲁棒性之间的负相关性可能是由于改变潮流的近似可达区域而引起的。能力悖论的存在是由于环状结构中关键边缘的复活能力增加而导致部分瘫痪。