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Power Laws in Real-World Networks


Erica Klarreich, in her article “Scant Evidence of Power Laws Found in Real-World Networks”, describes the controversy involving scale-free networks. Over the years, there has been numerous articles and journals published about the impact scale-free networks have and the ability of power laws to create uniformity between networks. Essentially, many individuals have used power laws to describe a common characteristic of specific networks. However, Klarreich delves into this analysis by pinpointing some of the faults of thinking of complex networks as scale-free, where scale-free describes the concept we learned in class where a few nodes have more connections than others. She goes through her article discussing the implications of the power law where there is no one scale that can work to characterize all networks.

She begins by describing how gaining knowledge of the architecture of scale-freeness and the ability to characterize different networks based on laws could help provide more information about different questions posed, for instance, how a virus is spread through a network. Klarreich also notes that some purely random networks, for example, do not follow these laws that we have discussed in class. During lecture, we had discussed how power laws can help see how there are imbalances in different networks, such as the network with the Web. However, Klarreich notes that a significant amount of datasets have shown networks, including social networks and aspects of the Web network, rejected a power law as a possible description for the structure of the network.

She delves into more examples where she argues that scale-freeness would be an ideal model for networks, but it fails to capture the actual behavior—it seems like it could work, but essentially the data does not favor this method. As we had mentioned in class, Klarreich also mentions how the “rich get richer and hubs get hubbier” when a new node joins the network. It is more likely to connect to a high-degree node rather than a low-degree one. Through these ideas, people must come up with a new method of creating an organizing principle for describing networks that all people agree on.

One of the main issues is the desire to create a universal characteristic to describe these networks. Nonetheless, Klarreich continuously describes how there is no universality of scale-free networks: each network in the real-world is in fact unique. Therefore, people must come up with new ideas, new methods, and new mechanisms to explain networks in a different manner than they have been doing from the past. Rather than getting stuck on trying to force an idea upon previous networks, develop new ways of analyzing them.


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