The Topology, Robustness and Vulnerability of Networks.

Breaking down of Networks

Node failure can easily break a network into isolated, non-communicating fragments. The 1996 blackout in the US highlighted the underlying vulnerabilities of the interconnectivity of the electrical network, and how a single disturbance can be detected thousands of miles away. There is a question asked, how many routers must we remove from the Internet to break it into isolated computers that cannot connect and communicate with each other?

As the Internet, the World Wide Web, the cell and social networks are known to be scale-free, it could be said that a significant number of nodes can be randomly removed from it without its breaking apart.

So what is the source of the topological robustness? The few highly connected nodes -- the hubs that keep these networks together is one of the main causes of this robustness. If failure of nodes have equal chances, small nodes are far more likely to be dismantled as there are so many more of them.

The accidental removal of a hub will not be fatal either, since the large hubs will maintain the network's integrity. Topological robustness is thus rooted in the structural unevenness of scale free networks: Failures disproportionately affects small nodes.

It is possible to take down networks, hackers can target and attack the hubs, taking large hubs down can cause networks to be slow as traffic now needs to flow to other hubs, and may eventually make the network fail.

The removal of the most connected nodes may however disintegrate these seemingly robust networks. In understanding the complex system, simulations have shown that one can remove many nodes from a key cellular network without the risk of killing the organism. If however, a drug or an illness shuts down the genes encoding the most connected proteins, the cell will not survive. If the highly connected keystone species are removed, the ecosystem dramatically collapses.

As seen in Social Media, Rockstars of Social Media are hubs. When they start to get on MySpace, they can bring a lot of following and crowd to join MySpace. They are opinion leaders, and when they think it is unsafe and they leave MySpace, there is also a large Exodus of members.

The price of topological robustness, however, is extreme exposure to attacks. Taking out hierarchy of highly connected nodes will break any system. It is bad news for our economic establishment as the failure of the financial giant, Freddie Mac and Fannie May would ripple and cause a widespread recession worldwide. On the Internet, this exploit allows hackers to design strategies that will take down the whole infrastructure.

Research has shown that topology, robustness and vulnerability cannot be totally separated from each other.

-- Robin Low