Disrupting Networks

Many guerrilla war tactics are not new. They’ve just grown more effective because economies are far more sophisticated and more vulnerable.

Infrastructure is one vulnerable network. The rest of the economy relies on communication, transportation, and energy networks. Information and resources flow through these networks. If critical nodes fail, or the links are severed, it causes a cascade failure throughout the economy.

Our infrastructure is built as a scale-free network. These types of networks are robust against a large number of random internal errors. However, hostile agents can observe the structure of scale-free networks and identify critical hubs. Scale-free networks are extremely fragile when under external attack.

Victor Davis Hanson wrote that ancient Greek hoplites could not do much damage to farmland. They couldn’t chop down, burn, or uproot olive trees for instance. It required far too much labor. The hoplites tried to interdict food supply into cities under siege instead.

The strategy was only mildly effective, but this was because of how primitive old economies were. Today, guerrillas can target electrical power stations and lines to shut off power in a city. They can do so at much lower cost and inflict vastly more damage.

Here’s one such attack to help you visualize the extent of network disruption attacks.

John Robb reports on the recent attacks on the Mexican Pemex oil piplines by a radical left-wing militant group. The guerrillas set off six explosions on the pipeline and this is the havoc they caused:

• Over 2,500 business will suffer severe harm in 11 of Mexico’s 32 states. 1,100 companies have shut down production. Key industries impacted: Auto, glass, food, and cement. For example: Volkswagen (1,780 cars a day, 81% of which is for export).
• Revised estimate of $200 million a day in costs.
• Impact expected to last for a week.

[Return on Investment] for an attack that cost less than estimated $10,000 to accomplish? Rough estimate: 1.4 million percent. Welcome to modern war.

Now here’s a somewhat technical explanation as to what is going on.

This is what a scale-free network looks like:

The nodes are sized according to the number of connections they have.

This was formed through preferential attachment. One node has 55 connections, but the vast majority of nodes have just one connection. This forms a power law distribution of links. It’s a very small network and it is hierarchical.

You can measure the efficiency of the network. How quickly can resources flow from one random node to another random node? That central hub makes the network very efficient. If you to reach another node, you can probably jump straight to that hub and reach the other node in one or two more jumps. There are minor hubs as well.

If this was a randomly distributed network, you would have to navigate through a maze of nodes to get anywhere.

Here’s a much larger Scale-Free networked compared to a random exponential network:

Again, notice the structural differences. Scale-free networks have more preferential attachments so there are more hubs.

It follows a power law of roughly P(k) ~ k^-y
The frequency is roughly y = 1/x when graphed. You can measure the number of links in each node by rank. The Nth position is 1/Nth. The second ranked node with have 1/2 as many links as the first ranked node. The third ranked node will have 1/3 as many links as the first. And so on.

Infrastructure networks tend to be built to fit around large social networks. So most infrastructure is congregated in and around cities where the bulk of the population is.

Social networks are more fluid and adaptable – people can move around or leave more often than fixed infrastructure.

Here’s a paper (with the above graph) about the susceptibility of the Internet to random errors and attacks by Barabási, Albert, Jeong.

They test the stability of scale-free and exponential networks. A random error is when a random node or connector fails. An attack is when a selected node fails. How does this impact flows within a system? How many removed nodes does it take for the system to catastrophically fail?

One way to measure efficiency is to measure the diameter of the network. You take two random nodes and measure the number of connections and nodes between them. A Scale-free network has a very low diameters at the start, so resources can flow through it quickly.

Scale-free networks are extremely robust against random errors

Thus even when as many as 5% of the nodes fail, the communication between the remaining nodes in the network is unaffected. This robustness of scale-free networks is rooted in their extremely inhomogeneous connectivity distribution: because the power-law distribution implies that the majority of nodes have only a few links, nodes with small connectivity will be selected with much higher probability. The removal of these ‘small’ nodes does not alter the path structure of the remaining nodes, and thus has no impact on the overall network topology.

Take the electrical grid. There are many internal errors, mistakes, and various problems, but the network is rarely effected. The grids can withstand a lot of mistakes before blackouts occur.

But here’s the catch. Central hubs are formed by preferential attachments. Hostile militants will also have a preferential attachment to attacking it.

To simulate an attack we first remove the most connected node, and continue selecting and removing nodes in decreasing order of their connectivity k. … When the most connected nodes are eliminated, the diameter of the scale-free network increases rapidly, doubling its original value if 5% of the nodes are removed. This vulnerability to attacks is rooted in the inhomogeneity of the connectivity distribution: the connectivity is maintained by a few highly connected nodes ( Fig. 1b), whose removal drastically alters the network’s topology, and decreases the ability of the remaining nodes to communicate with each other.

A planned attack disrupts the network. Continual planned attacks can virtually shut it down without having to hit a large number of nodes. They just have to strike central hubs and major connection points.

So infrastructure is robust against internal errors and mistakes but is very fragile when attacked.

Networks emerge through self-organization and they regenerate through the same means. The resilience of networks is based partly on the sheer number of connections and partly based its small-worlds nature. Redundancy provides stability even with a large number of random errors. When nodes, hubs, and edges are removed, the network is only temporarily disrupted. Flows of resources and information are redistributed to different nodes through new or different edges.

Take a traffic model. Say there is a traffic jam on the avenue. Instead of sitting in traffic, you turn off the main road and head down the side roads. That’s a load redistribution. Traffic engineers try to account for that type behavior.

Also note that all roads do not have the same “capacity.” One-way side-streets cannot carry as many cars as a 6-lane highway.

Here’s another paper about network disruption. It analyzes attacks on communication and transportation networks (pdf).

Most of the communication/transportation systems of the real world can be represented as complex networks, in which the nodes are the elementary components of the system and the edges connect pair of nodes that mutually interact exchanging information. To quote a few examples: in the Internet the nodes are the routers and the edges (or arcs) are the cables connecting couples of routers; in an electrical power grid the nodes are the substations (generators or distribution substations) and the edges are the transmission lines; in a city road system the nodes are the crossings and the edges are the roads; and in transportation systems considered on a larger scale, the nodes are the cities and the edges are the highways or the flights connecting a couple of cities.

They compare a scale-free network and a random exponential network of 2000 nodes and 10,000 connections each and test them against error and attack.

The Scale-free network outperformed the exponential network in minimizing the damage caused by errors. Yet the scale-free network was ruined after just a few attacks.

The authors here ran the same test again with load-redistribution factored in. Surprisingly, it changed little. Load-redistribution does not improve the ability of a network to withstand attack. It’s not really possible in the structure. The loss of a central hub cannot be easily replaced if all things were equal. Generally, the central hubs also have the most capacity, so the new replacements cannot carry as many resources.

There are many infrastructure networks which are scale-free and are highly vulnerable to guerrilla attacks
-Electricity
-Water
-Transport (Airlines, Subways, Railways, Bridges)
-Telecommunications
-Energy and Fuel

And there’s more.

The thing is, once basic infrastructure is lost, the rest of the economy cannot function. Loss of water supplied by destroying pipelines and aqueducts could devastate a city, especially if it is a desert city like in the Mid East. Loss of electricity shuts down factories, hospitals, schools, etc.

A few $10,000 attacks can cause billions of damages and temporarily shut down entire state economies.

Welcome to the Brave New War