Network Resilience: Single Points of Failure and Targeted Attacks
Which sites and links can a network not afford to lose? How the lab finds them, and what its numbers can and can’t tell you about real operations.
Why some failures matter more than others
Most operations depend on a network. A plant depends on its suppliers, a hospital on its computer systems, and a city on its roads and power lines. Picture each site, supplier or system as a dot, and each dependency as a line between two dots. When one dot fails, everything that passed through it needs another route. Usually there is one. Sometimes there isn’t, and part of the network gets cut off from the rest.
The useful question is which single site or link you can’t afford to lose. Counting links doesn’t answer it. A site with only two links can still be the only bridge between two groups. I built the lab to show this. It’s a small network of 22 nodes (the dots) in four clusters, joined by 39 links. You can remove any link or node and watch every number update. You can also compare random breakdowns with a targeted attack. The attack always knocks out the busiest crossroads next: the node that the most shortest routes run through. Where a node sits on the screen doesn’t matter. No number depends on it.
Three ways to measure importance
Degree is the number of direct links a node has. It’s easy to count, but it says nothing about what lies past those links. Betweenness centrality measures how much of the network’s routing runs through a node. Take every pair of other nodes and find their shortest routes. Then add up the share of those routes that pass through this node. A busy crossroads scores high. The measure assumes traffic always takes a shortest route. An articulation point is a single point of failure: a node that, removed on its own, splits the network into more pieces. In math terms, removing it increases the number of connected components (separate pieces) in an undirected graph (a network whose links work both ways).
What the attack test shows
Remove an important node or link, and the network can break into pieces or routes can get longer. The attack test makes this clear. It removes nodes in order of betweenness, recalculating the scores after each removal. After just 4 removals, the biggest connected piece has shrunk to half its starting size. Random failures take longer. Averaged over 400 random failure orders, it takes 8 or 9 removals, depending on the seed (9 at the lab’s default seed). The seed is the starting number for the random draws. These results describe the shape of the network. They don’t automatically predict how much production you’d lose. What it means for real work depends on what the dots and lines stand for. It also depends on whether a backup route can really do the same job.
What the model leaves out
A few things the lab ignores can change the answer a lot. Links can run one way only. They can have weights, like distance or cost, and limits on how much they carry. And a network’s behavior changes over time. The lab’s network is tiny on purpose, so it’s easy to read. A real company’s map of what depends on what needs clear definitions of what each dot and line means. It often needs methods built for one-way or weighted links, too.
How I check it
Removing an articulation point should always split the network into more pieces, since that’s what the term means. The intact lab network has none. So no single failure cuts it apart until your own edits create one. Betweenness has to be recalculated after every change to the network, because old scores describe the old network, not the new one. In the lab, an attack that keeps its first betweenness ranking does less damage over the whole run than one that recalculates after every removal. Its robustness score is 0.275, against 0.205, and higher means the network held together better. Any measure should also be tested on small networks with known answers before you trust it on big ones.