Thursday, November 18, 2010
Albert-Laszlo Barabasi: Linked (2002)
Albert-Laszlo Barabasi’s Linked is a popular introduction to “the new science of networks.” According to Barabasi, one of the field’s major scientific contributors, much of 20th-century science was aimed at decomposing objects of study into their simplest components. Despite its many accomplishments, this reductionist approach prevented science from realizing how “everything is linked to everything else.” In the last decade or so, however, “We have come to grasp the importance of networks.” We now recognize that “[n]etworks are present everywhere” and “that amazingly simple and far-reaching natural laws govern the structure and evolution of all the complex networks that surround us.” The theory of networks began with Leonhard Euler’s creation of graph theory. Around 1736, Euler innovatively answered a trivial question about whether it was possible to walk once across all of the bridges connecting an island in Konigsberg to the rest of city without re-crossing any of the bridges. Euler approached this mathematical problem by “viewing Konigsberg’s bridges as a graph, a collection of nodes connected by links.” By treating the bridges as a network, Euler was able to clearly and definitively solve the problem. A more recent and influential contribution to the theory of networks came from the mathematician Paul Erdos, who around 1959 “laid the foundation of the theory of random networks.” Ignoring the diversity of natural examples, Erdos created a general model of complex networks by constructing a graph through randomly connecting nodes. Because links are formed randomly in this model, most nodes have the same number of links. “We obtain a network with a very uniform fabric in which the mean is the norm.” The simplicity of this random network theory made the model extremely appealing, and helped it dominate thinking about networks for decades. “[The model] equated complexity with randomness. If a network was too complex to be captured in simple terms, it urged us to describe it as random.” In 1967, the sociologist Stanley Milgram made another contribution to the theory of networks that later would be popularized in a play as the “six degrees of separation.” Milgram performed a study asking, “how many acquaintances would it take to connect two randomly selected individuals?” The answer was shockingly low: 5.5. “Stanley Milgram awakened us to the fact that not only are we connected, but we live in a world in which no one is more than a few handshakes from anyone else. That is, we live in a small world. Our world is small because society is a very dense web.” More recent research has demonstrated that the smallness Milgram discovered is the norm, not the exception, in networks. “’Small worlds’ are a generic property of networks in general. Short separations is not a mystery of our society or something peculiar about the Web: Most networks around us obey it.” In the 1960s and 70s, another sociologist, Mark Granovetter, discovered that “[w]hen it comes to finding a job, getting news, launching a restaurant, or spreading the latest fad, our weak social ties are more important than our cherished strong friendships.” Granovetter demonstrated that, in the terms of graph theory, nodes tend to be clumped in clusters, in which each node is linked to all the others in the cluster (for example, a group of friends), and that only a few long links (such as relationships with passing acquaintances) connect the nodes of different clusters. Further research on clustering by Watts and Strogatz proved that only a few of these distant links are needed to turn a network with clusters into a small world in which the number of links between any two nodes is relatively small. The existence of clusters initially seemed to contradict the even network texture described by random network theory, though Watts and Strogatz were ingeniously able to reconcile the two. But random network theory faced a more fatal challenge when Barabasi and his colleagues, attempting to map the Web, discovered the existence of hubs. To their surprise, the robot they sent out across the Web came back with “evidence of a high degree of unevenness in the Web’s topology.” Their research showed that the “architecture of the World Wide Web is dominated by a few very highly connected nodes, or hubs.” Although first recognized on the Internet, hubs are not limited to the Web. “Hubs appear in most large complex networks that scientists have been able to study so far. They are ubiquitous, a generic building block of our complex, interconnected world.” In fact, “large hubs . . . fundamentally define [a] network’s topology.” The discovery of hubs indicated that the distribution of links in networks does not follow a bell curve, where large deviations from some norm/average number of links would be rare if not unthinkable. Instead, the distribution of links adheres to a power law. “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.” Because of this power law distribution, there is no average scale to such networks, but rather a “continuous hierarchy of nodes.” Erdos’s random network model therefore was replaced by a scale-free network model, which Barabasi and his colleagues have devoted their efforts to developing. Work on the scale-free model soon addressed the issue of growth, a feature of networks neglected by the random network model. Hubs form as networks grow because of “preferential attachment.” “Network evolution is governed by the subtle yet unforgiving law of preferential attachment. Guided by it, we unconsciously add links at a higher rate to those nodes that are already heavily linked.” Growth combined with preferential attachment gives the first nodes in the network a competitive advantage, since they have more time to accumulate links that make them attractive to nodes appearing later. But this model was obviously reductive, ignoring the creation of internal links or the deleting of older links, and it also could not explain how latecomers—such as Google—could become hubs. One problem was the model treated all nodes as if they were the same. So a concept of “fitness,” the attractiveness of a node, was added to the model. Although growth and preferential attachment were still the dominant laws, the addition of a category for fitness modified the model so that “[b]etween two nodes with the same number of links, the fitter one acquires links more quickly.” However, fitness was not enough to explain how some hubs, such as Microsoft, come to completely dominate a network. A supplementary network model based on the concept of “condensation” was needed to explain this elimination of competition in a network. So in some cases, behavior on the network “destroys the hierarchy of hubs characterizing the scale-free topology, turning it into a starlike network, with a single node grabbing all the links. . . . A winner-takes-all network is not scale-free. Instead there is a single hub and many tiny nodes.” Further research on networks has addressed issues relating to network strength and failure. Scale-free networks show “topological robustness”: “a significant fraction of nodes can be randomly removed from any scale-free network without its breaking apart.” This “[t]oplogical robustness is . . . rooted in the structural unevenness of scale-free networks: Failures disproportionately affect small nodes.” But this same topology makes networks vulnerable to attack, since hubs play such a major role in maintaining the network. “Disable a few of the hubs and a scale-free network will fall to pieces in no time.” In other words, “scale-free networks are not vulnerable to failures. The price of this unprecedented resilience comes in their fragility under attack. The removal of the most connected nodes rapidly disintegrates these networks, breaking them into tiny noncommunicating islands. Therefore, hidden within their structure, scale-free networks harbor an unsuspected Achilles’ heel, coupling a robustness against failures with vulnerability to attack.” Hubs also make networks susceptible to “cascading failure,” in which the failure of a major node shifts that node’s responsibilities onto other nodes, overwhelming them and causing them to also fail, creating a pattern of failure that spreads across the network. Recent mapping of the Web has underscored that it is a “directed network”: links often only take you in one direction. “[T]he most important consequence of directedness is that the Web does not form a single homogeneous network. Rather, it is broken into four major continents, each forcing us to obey different traffic rules when we want to navigate them.” There is an “easily navigable” central core containing the major websites. There are then “in” and “out” continents, the former easily taking you into the core (but not back out), the latter easily taking you out of the core (but not back in). Largely disconnected from the core and these continents are islands and tendrils. The directedness of the Web makes it difficult, if not impossible, to accurately map it (robots are unable to find nodes on the “in” continent or islands). This fragmented shape of the Web might seem rather unique or contingent, but its pattern is typical of all directed networks. In his final chapters, Barabasi considers how a wide range of social, biological, and economic topics can profitably be treated as networks. His reduction of complex phenomena to network models becomes quite problematic in the chapter on business. Unsurprisingly, he repeats post-Fordist clichés about firms becoming lean, flat, and flexible, in other words, becoming networks. On a more macroeconomic scale, he also asserts, “the market is nothing but a directed network. Companies, firms, corporations, financial institutions, governments, and all potential economic players are the nodes. Links quantify various interactions between these institutions, involving purchases and sales, joint research and marketing projects, and so forth. . . . The structure and evolution of this weighted and directed network determine the outcome of all macroeconomic processes.” According to this network logic, economic crises are due to cascading failures. He even claims, “Understanding macroeconomic interdependencies in terms of networks can help us to foresee and limit future crises.” Although there is some truth to this equation of markets and networks (see the work of economics-oriented actor-network theorists like Michel Callon or Donald MacKenzie for better examples), Barabasi here risks naturalizing post-Fordist, neoliberal capitalism. By importing scientific “laws” into economics, Barabasi makes a contingent economic formation seem like an objective necessity, and he limits resistance to that economic system to the range of behavior described by a network model.