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Scale-free Networks

The study of networks emerged because researchers wanted to understand better about how a variety of complex networks in our lives would form and behave. Networks can be found everywhere in our lives; friendship or webpages linked by hyperlinks are the most well-known examples. We can also find networks in life sciences too; protein-to-protein interactions can be considered a network in which two or more protein components are linked by biological interactions. In the early steps of the study, researchers believed that every type of network would form randomly. That is, two nodes would be connected by a randomly generated link between them. Therefore, each node was generally expected to be connected to the same number of nodes. This notion prevailed until 1998 when researchers from the University of Notre Dame found that a network usually has two different sets of nodes: one with only a few connections and the other with a large number of them. This is not so surprising when you think of webpages. For instance, Yahoo is connected to a huge number of webpages like news, weather, mail and so on whereas personal pages have a relatively limited number of connected webpages. Researchers decided to name the nodes like Yahoo as hub and the networks with these hubs as scale-free networks (because the hubs are linked to the large number of links with no bound).

The existence of scale-free networks is generally explained by two main reasons: “growth” and “preferential attachment.” It is obvious that the nodes which existed longer in the network had more chance to get connected by newly introduced nodes. Also, those new nodes are likely to be introduced to the networks by hubs. (Someone surfing on the Internet will usually begin from Yahoo or Google.) In the meantime, the properties of scale-free networks produce both advantages and disadvantages to the networks themselves. As shown in the first row of the diagrams below, when a disruption is present, the randomly connected network is broken into several pieces. This is not be a favorable case if the links represent the roads and the nodes are the cities. In the event of an earthquake, those isolated cities would not be able to receive emergency supplies properly. Yet, as the second row of diagrams show, most of the nodes would still be connected to one another in scale-free networks. However, most of the nodes in the scale-free networks would not always survive in the event of a disruption: as shown in the third row of the diagrams, if a disruption attacks a node with many connected nodes to it, the effect would be severe.

 

Not all networks are the scale-free networks, such as a crystal lattice. However, many networks have the hubs and understanding this type of networks improves many aspects of our lives. For example, in the previous example of the earthquake, researchers realized the vulnerability of the hubs and decreased the number of these hubs within the network. In such a way, they could decrease the chance that the disaster would affect those hubs and destroy the entire road network.  Knowledge of these complex networks has been extensively elaborated upon over the last decades and the study of networks should continue as long as they affect our lives.

Source: http://www.scientificamerican.com/article.cfm?id=scale-free-networks

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