Dynamics of node cascading model with source-sink edges

The load is a very important physical quantity for cascading failures in critical infrastructure networks. However, in previous studies, regardless of the node cascading failure model or the edge cascading failure model, all load in the network is born on the nodes ignoring the possibility of load pouring into the network from edges. For example, almost all vehicles from communities, units, parking lots, etc. are flooding into the transportation network from roads. To this end, considering that the starting point and the destination of the transferred load are located on the “edge†, we give a new method to calculate the initial load on the node and construct a node cascading model with source-sink edges. According to the information about the degree of two nodes connecting the edge, we define the edge weight and give the preferential mechanism of load destination selection. In addition, different from previous models, the load transmitted between two edges will be evenly distributed on all nodes of the shortest paths. By removing the node with the highest load in some artificial networks and two real networks, we study the cascading dynamics. We find the interesting phenomenon of the capacity paradox that the higher capacities of all nodes do not mean that the network has the higher robustness. By two metrics to quantify the network robustness, we further evaluate the robust mode of the network under different parameters, and study the optimal cost to suppress cascading failures in some networks.