March 14, 2011

Jodi Dean on hubs, notes, networks and the power-law.


Recent developments in network science demonstrate structure in seemingly random networks. On the web, for example, sites are not equally likely to have the same number of links. Nor are links randomly distributed among sites in a predictable, bell-curve fashion. Instead, there are clusters and hubs wherein some sites are nodes to which many sites link. These hubs serve as connectors for other nodes. In his path-breaking work on structure in complex networks, Albert-László Barabási finds hubs on the Web, in Hollywood, in citation networks, phone networks, food webs in ecosystems, and even cellular networks where some molecules, like water, do much more work than others.

Barabási explains that degree distribution in networks with hubs, most real networks, follows a power-law. He writes, “Power laws mathematically formulate the fact that in most real networks the majority of nodes have only a few links and that these numerous tiny nodes coexist with a few big hubs, nodes with an anomalously high number of links. The few links connecting the smaller nodes to each other are not sufficient to ensure that the network is fully connected. This function is secured by the relatively rare hubs that keep real networks from falling apart.” In most real networks, nodes don’t have an average number of links. Rather, a few have exponentially more links than others. Barabási describes the difference between random networks and networks that follow a power-law degree distribution with the term scale. In random networks, there is a limit to the number of links a node can have as well as an average number of links. Random networks thus have a characteristic of “scale.” In most real networks, however, “there is no such thing as a characteristic node. We see a continuous hierarchy of nodes, spanning from the rare hubs to the numerous tiny nodes.” These networks don’t scale. They are “scale free.”

Barabási notes that others have observed power-law degree distributions. The Italian economist Vilfredo Pareto noticed that 20 percent of his peapods produced 80 percent of the peas – nature doesn’t always follow a bell curve. He also found that 80 percent of the land in Italy was owned by 20 percent of the population. In business management circles, Pareto’s law is known at the 80/20 rule (although he did not use the term) and is said to apply in a variety of instances: “80 percent of the profits are produced by only 20 percent of the employees, 80 percent of customer service problems are created by only 20 percent of customers, 80 percent of decisions are made during 20 percent of meeting time, and so on.” Further examples might be Hollywood’s “A list” or the “A list” that emerged among bloggers. Like scale-free networks, Pareto’s law alerts us to distributions that follow power-laws.

How can power-laws be explained? Is some kind of sovereign authority redirecting nature out of a more primordial equality? Barabási finds that power-laws appear in phase transitions from disorder to order (he draws here from the Nobel prize-winning work of the physicist Kenneth Wilson.) Power-laws “are the patent signatures of self-organization in complex systems.” Analyzing power-laws on the web, Barabási identifies several properties that account for the Web’s characteristics as a scale-free network. The first is growth. New sites or nodes are added at a dizzying pace. If new sites decide randomly to link to different old sites, old sites will always have an advantage. Just by arriving first, they will accumulate more links. But growth alone can’t account for the power-law degree distribution. A second property is necessary, preferential attachment. New sites have to prefer older, more senior sites. Differently put, new sites will want to link to those sites that already have a lot of links. They don’t link randomly but to the most popular sites which thereby become hubs. Barabási argues that insofar as network evolution is governed by preferential attachment, one has to abandon the assumption that the Web (or Hollywood or any citation network) is democratic: “In real networks linking is never random. Instead, popularity is attractive.” Nodes that have been around for awhile, that have to an extent proven themselves, have distinct advantages over newcomers. In networks characterized by growth and preferential attachment, then, hubs emerge.

The fantasy of abundance – anyone can build a website, create a blog, express their opinions on the internet – misdirects some critical media theorists away from the structure of real networks. Alexander R. Galloway, for example, emphasizes “distributed networks” that have “no central hubs and no radial nodes.” He claims that the internet is a distributed network like the U.S. interstate highway system, a random network that scales, to use Barabási’s terms. Embracing Gilles Deleuze’s and Félix Guattari’s image of the rhizome, Galloway notes that in a rhizome any point can be connected to any other; there are no intermediary hubs and no hierarchies. For him, the Web is best understood rhizomatically, as having a rhizomatic structure. Barabási’s work demonstrates, however, that on the Web, as in any scale-free network, there are hubs and hierarchies. Some sites are more equal than others. Imagining a rhizome might be nice, but rhizomes don’t describe the underlying structure of real networks. Hierarchies and hubs emerge out of growth and preferential attachment.

- Jodi Dean, Democracy and Other Neoliberal Fantasies


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