This lecture’s topic was percolation and network resilience. We want to answer the questions of if a given fraction of nodes or edges are removed from a network , how large the connected components are or what the average distance between nodes in the components is. While removing nodes or edges we should consider some points. In bond percolation each edge is removed with probability (1-p). Causing the most damage to the network with the removal of the fewest edges is targeted attack. Usually edges with high betweenness are the targets to make the most damage to network.
Percolation threshold in an Erdos-Renyi graph is the point at which the giant component emerges.
Another fact about the resilience is scale-free networks are resilient with respect to random attacks. However they are not resilient against targeted attacks. Removal of successfully chosen a small number of nodes may cause many more nodes (their neighbors) to be disconnected to the network.
In power grid structural networks each node has a load and a capacity that says how much load it can tolerate. When a node is removed from the network its load is distributed to the remaining nodes. If the load of a node exceeds its capacity then the node fails. Hence we can conclude that network resilience depends on topology of the network.
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