Authors: Alex Tee Neng Heng, David G. Green

Here we presents simple model for simulating cascading failure on complex network. The breakdown of a node can unbalance the flow of the network and causes load redistribution to other nodes. If these nodes are overloaded by the extra load, this will be redistributed in turn. This sequence of overloading is sufficient to cause global system failure.

The nodes are the power stations, each of which can be in one of two possible states:

• Healthy (current load <= maximum load)

where maximum load = tolerance * initial load

A load on each power station is defined by the sum of all the shortest path length between the source and all other power stations. The shortest path is a path between 2 power stations such as that the sum of the efficiency (weight) of its constituent edges is maximised.

When a power station is overloaded, the efficiency of the edges connected to the node drop and the extra load is pushed to the nearby power stations. They also become overloaded and redsitribute their load onto other power stations.

### How to use the simulation

On the control panel on the right, selects the type of network to generate.

• Random. Connectivity (0 – 1)
• Tree. Branches (>= 2)
• Small world. K (>= 1) and shortcut (0 – 1)
• Scale free.

You can also configure other settings:

• Number of nodes (>= 5): the number of power stations in the network
• Tolerance (> 0): used to calculate maximum load for each power station.
• Target node: the type of node to be removed at the start of a simulation.
• Richest node: Node with the highest degree
• Random node: Any node in the network
• Poorest node: Node with the lowest degree