Scale-free law: network science and copyright.

• Author: Gonzalez, Andres Guadamuz
• Position: Symposium: Interdisciplinary Conference on the Impact of Technological Change on the Creation, Dissemination, and Protection of Intellectual Property

1. INTRODUCTION

   One common feature of literature dealing with new technologies, and particularly those authors dealing with any legal aspect of cyberspace, is to over-emphasize the importance of information and communication technologies to our present situation. This has led to an abundance of commonplaces that are just variations of the phrase "the Internet has changed everything." While it is useful to distance oneself from such cliches, this essay will unfortunately begin with a variation of this theme. Commonplaces exist for a reason, and in the areas of copyright law and the study of networks, the Internet has indeed changed everything.

   Networks are everywhere. The staggering complexity and seemingly chaotic nature of everyday life is actually a collection of different interactions. We are constantly surrounded by the social network, the financial network, the transport network, the telecommunications network, and even the network within our own bodies. The understanding of how these systems operate and interact with one another has been the realm of physicists, economists, biologists, and mathematicians. Until recently, the study of networks was left to theoretical and academic debates as it lacked proper empirical application because it was difficult to gather reliable data about large and complex systems. But in recent years, the Internet has given researchers the opportunity to study and test the mathematical descriptions of the vast complex systems. The growth rate and structure of cyberspace allows researchers to map and test several previously unproven theories about how links and hubs within the network interact with one another. With the Web, we now have means to test the organizational structures of networks, their architecture, their growth, and even allow some limited predictions about their behavior, strengths and vulnerabilities.

   With the increasing reliability on the descriptive--and sometimes predictive--nature of network science, a logical next step for legal scholars is to look at the potential legal implications of some of the characteristics of networks. Some academics and practitioners have started finding potential uses for network science tools; efforts that will be highlighted in following pages. One particular topic of interest where network science could have a noticeable effect is the area of the regulation of the Internet, which has provided ample possibilities for discussion and analysis during its short existence. (1) Some of the most interesting legal literature from the early days of the modern Internet (2) deals with the potential difficulties in putting a leash on the chaotic and anarchic nature of cyberspace. The skepticism about the impossibility to generate any effective type of regulation has prompted some authors to theorize about how to exercise control over the online world. (3) This debate left some unanswered questions, particularly in the area of intellectual property rights, where the enforcement of copyright in the digital domain has become an increasingly difficult issue.

   It is in this legal context where the present article will attempt to make use of the study of self-organized scale-free networks in order to make use of the improved understanding of how networks are formed, grow and operate, and apply it to problematic regulation of copyright in cyberspace.

2. THE NETWORK SCIENCE REVOLUTION

   It would be easy to overestimate the importance of network theory in the real world by stressing the importance of the Internet to our everyday lives; however, such assumptions would be missing the fact that the study of networks is not a new science. The understanding of how networks operate and interact with one another has been studied by physicists, economists, and mathematicians for centuries. (4) Many operational assumptions and theories of networks, however, had not been applied by other disciplines. Some earlier works on the topic described specific network architectures and characteristics, but the studies were smaller-scale, although they set the theoretical principles for what was to become the modern discipline. (5)

   In recent years, the Internet has given researchers the opportunity to study and test several of the existing mathematical descriptions of complex networks. (6) Although the Web is composed of billions of pages, its fast growth-rate and international reach allow researchers to map and examine several previously untested ideas about how networks interact. With a combination of the characteristics of online hyper-linking, and the help of spiders and web crawlers, (7) researchers have the means to test the organizational structures of the architecture and behavior of networks.

   Much of the current interest in networks can be traced back to a series of popular science books dedicated to publicizing the latest developments in research. Titles of note are Linked by AlbertLaszlo Barabasi, (8) The Tipping Point by Malcom Gladwell, (9) Critical Mass by Philip Ball, (10) and Six Degrees by Duncan J. Watts. (11) These "pop science" credentials could make those unfamiliar with the literature suspicious about the validity and reliability of network theories, (12) but this skepticism would be misplaced, as most of these books have sound peer-reviewed research behind them, and in most instances they have been written by the primary investigators themselves.

   The modern understanding of networks begins with the study of statistical phenomena called power laws, described as "[w]hen the probability of measuring a particular value of some quantity varies inversely as a power of that value." (13) In other words, power laws are tools that describe the divergence in the predictable and average value of an observable fact. Most natural phenomena display "normal" distributions, which when plotted in an axis display a bell-shaped form. In a normal distribution, the largest number of instances is encountered in the middle. Most people are average height, while there are small numbers of both very short and very large people; charting such distribution will provide a bell-shaped curve. (14)

   Power distributions, however, do not follow the normal trend; in them we find that there are few remarkable instances that account for a very large number of occurrences of the studied event. Because of this, a power law distribution does not have a peak, but the line charting given incidences of an event tend to drop off sharply, which indicates the increased likelihood of extreme events. (15) An example of power law distributions can be found in city populations. If we are counting all of the people living in cities around the world, we will soon discover that megalopolis like Tokyo, Mexico City, New York, and Mumbai account for a disproportionate amount of the total city inhabitants. These cities generate tell-tale spikes in the data, accompanied by a long tail of smaller populations.

   Power laws often display what is known as Pareto distributions, (16) or the 80/20 rule, following the popular perception that 80 percent of the work is performed by 20 percent of the employees; or that 80 percent of the wealth is held by 20 percent of the population. (17) A Pareto distribution, named after economist Vilfredo Pareto, is used to describe large inequalities in data, where most of the distribution is concentrated in a relatively small portion of the graph.

   It may be surprising that power laws seem to be found in all sorts of circumstances outside of what is normally perceived as a network, including biological systems. (18) Other places where these networks have been found are, according to Newman:

   In addition to city populations, the sizes of earthquakes, moon craters, solar flares, computer files and wars, the frequency of use of words in any human language, the frequency of occurrence of personal names in most cultures, the numbers of papers scientists write, the number of citations received by papers, the number of hits on web pages, the sales of books, music recordings and almost every other branded commodity, the numbers of species in biological taxa, people's annual incomes and a host of other variables all follow power-law distributions. (19) A corollary of power laws is that this type of distribution may produce scale-free environments. In a normal distribution, there is little or no room for results that are considerably above and below the norm. In a plot of people's heights, one will expect to find that most people are average, with deviations towards both ends, thus forming a bell when charted. In a scale-free environment, most people would be average height, while there would be some thirty and fifty meter giants walking around, and from time to time you could even encounter a person measuring hundreds of meters. (20)

   Power laws and scale-free topologies apply to networks in general, but they seem to be more prevalent in large-scale complex systems. (21) In order to chart vast networks, one must understand some of the basics of how they operate. Most networks are composed of three elements: nodes are individual elements in the network; links are the relations between nodes; while hubs are collections or clusters of nodes. (22) In a normal network distribution, we would expect to find that nodes are distributed in an average manner, some with more links, and some with fewer links; this generates a random chart. In a scale-free network, the vast majority of nodes and hubs have an average or small number of links, while very few hubs will have an exceptionally large number of links, forming super-nodes, or even super-hubs. (23)

   Thanks to the wealth of innovative research into networks, the architecture of the Internet is now understood enough to claim that it presents many of the inherent characteristics of scale-free networks and, therefore, it can be said that it responds to power laws. The topology of the Internet has allowed its study by providing researchers...