Faster growth heightens Web class divide

By Kimberly Patch, Technology Research News

It is clear that the World Wide Web is continuing to grow very quickly, and it is also clear that there is a pattern to the growth. Many research efforts are aimed at figuring out why the Web grows exactly the way it does in order to better plan Web-based efforts like electronic commerce.

Researchers from Korea have put together a mathematical model of the Web that shows that the rate of increase in the number of Web sites influences the pattern of Web growth. One effect is that the faster a segment of the Web grows, the sharper the distinction between its large and small sites -- the haves and have-nots of the Internet.

Measurements of the Web have shown that the number of Web sites increases exponentially with time, and that the growth of the Web has a power law, or scale-free structure, with a few Web sites, or nodes, that have many connections to other nodes, and many nodes that have few connections.

To account for the power law behavior, modeled the interactions among Web sites as an external force acting on any given Web site. Mathematically, this force has both a range and a strength, said Chang-Yong Lee, an assistant professor at Kongju National University in Korea.

Because any Web site can be accessed within a few clicks of a mouse from anywhere else on the Web, there is no spatial limitation to the force range. This is in contrast to the brick and mortar world, where a customer living near a more expensive store is likely to buy an item there rather than at a cheaper but more distant store, said Lee. "For the Web sites on the Internet, however there is no such [geographical] barrier," he said.

Instead, a site's popularity depends on the popularity of all the other Web sites, said Lee. "The force has to be global in the sense that any Web site can act... on any other Web site."

The strength of the force varies in time due to characteristics like Internet topology and changes in traffic, said Lee. Because it is difficult to take into account all the factors that influence the strength of a Web site's popularity, the researchers lumped them together by mapping them all into a time variable.

The model contained one more variable -- the growth of the number of Web sites, said Lee. "The number of Web sites at each time step is not fixed, but grows exponentially," he said.

When the researchers used the model to run a simulation of the Web, the simulation reflected most of the important characteristics of the real-world Web, according to Lee. It showed the expected power law structure of links, or visitors to Web sites, and also showed the known relationship between age and Web site popularity, he said. "As time progresses, [a given] Web site will be known to more Web surfers, [and] thus have more popularity."

The model also showed that the strength of the cumulative effects of interactions among sites -- the external force -- influences the relationship between a Web site's age and its popularity, said Lee. The bigger the strength, the less dependence between age and popularity, he said.

The most surprising result, however, is that the exponent, or curve of the power law structure is directly related to the growth rate of the number of Web sites in the model, meaning the faster the network grows, the bigger the difference between the large and small nodes, said Lee.

This means that different segments of the Web that have different growth rates also have different power law curves. For example, when numbers representing the Web as a whole and the .edu portion of the Web are plotted on a graph, with one axis showing the number of sites and the other axis showing site size, the steepness of the curve connecting these numbers is different for the two categories.

Within the researchers' model, this variation can be explained by looking at different growth rates of the number of Web sites for each category, said Lee. "The larger the growth rate, the bigger the exponent," he said. In graphical terms, the power law curve gets steeper as the growth rate increases, making the overall growth rate curve for the Web steeper than the curve representing just the .edu domains.

The Web is essentially a competitive, complex system that is always changing as the number of Web sites increases exponentially, according to Lee. The global interaction of the system and its dynamic nature are the two main ingredients that determine its structural characteristics, he said.

The researchers' model may capture some properties of the .edu domain, but the work doesn't necessarily carry over to the general network, said Bosiljka Tadic, a physics professor at the Jozef Stefan Institute in Slovenia.

The research results are potentially interesting for the .edu domain, which has a power law distribution close to that of the model, said Tadic. The model could be used to estimate the "projected number of visits given that the trends in growth of the number of nodes are known," he said.

Lee's research colleague was Seungwhan Kim, of the Korean Electronics and Telecommunications Research Institute. They published the research in the March, 2002 issue of the journal Physical Review E. The research was funded by The Korea Science and Engineering Foundation (KOSEF).

Timeline:   < 5 years
Funding:   Government
TRN Categories:   Internet
Story Type:   News
Related Elements:  Technical paper, "Dynamic Model for the Popularity of Websites," Physical Review E, March, 2002.


June 12/19, 2002

Page One

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Faster growth heightens Web class divide

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