Networks in a wide range of application areas have been shown to exhibit scale-free topologies, including social networks, the world wide web, the Internet, semantic networks, and biological networks. Their scale-free nature be driven by preferential attachment as the network grows.
As one example, it is interesting to learn how researchers measure and analyze the topology of the Internet (e.g. the CAIDA, DIMES and RouteViews efforts). The CAIDA mapping/analysis team publishes an interesting Internet network visualization, and even has some older animated graphs illustrating the dynamics of the network over an 18 month period.
Some interesting implications of scale-free networks are that a number of key nodes, known as 'hubs', exhibit a much higher than average connectivity; that the networks are generally very robust to random failures; and that they are particularly sensitive or vulnerable to failures at the hub nodes.
How this general information is put to use depends on the application:
- communications engineers use it to analyze and construct robust networks
- militaries may target key individuals in order to disrupt terrorist networks
- and not surprisingly, marketers can exploit 'hubs' identified within social networks for targeted advertising
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