Study reveals Net's parts

By Kimberly Patch, Technology Research News

As the Internet grows, it is becoming increasingly important for software makers and information managers to adapt to the network's basic patterns rather than its current configuration. Researchers studying the workings of the Internet have found several of its structural secrets, but Internet simulations still differ from the real thing.

Researchers from the Nordic Institute for Theoretical Physics in Denmark, Brookhaven National Laboratory, the Niels Bohr Institute in Norway, and the Norwegian University of Science and Technology have uncovered another fundamental Internet attribute -- it has an underlying modular structure regulated by the number of sites, or nodes, that link to a given node.

The researchers used a method similar to the algorithm underlying the search engine Google to measure Internet modularity. But rather than the usual method of measuring connected nodes, the researchers focused on links between nodes, mapping out a picture of links linking to links.

They found that the Internet has about 100 modules that correspond roughly to countries, and the farthest points from each other are Russia and U.S. military sites, according to Kasper Astrup Eriksen, who carried out the research at the Nordic Institute for Theoretical Physics and is now a researcher at Lund University in Sweden.

The work promises to improve the accuracy of Internet simulators, and could help strengthen the Net by pointing out where to reinforce links between weakly-connected modules.

Past research has shown that the Internet is a scale-free network, meaning it has a few well-connected nodes and many nodes with only a few links. "For the Internet the rule is approximately... for every 1,024 nodes with one link, there are 256 nodes with two links, 64 nodes with four links, 16 nodes with eight links, four nodes with 16 links, etcetera," said Eriksen.

In general, scale free networks exhibit preferential attachment, meaning the more links a node already has, the more rapidly it will collect additional links. If a node has two existing links, for example, it is twice as likely to be linked to again than a node with only one existing link.

The Nordic/Brookhaven/Niels Bohr team looked at the structure a little differently, focusing on links between nodes rather than the nodes themselves. Connections can be thought of as being between links rather than nodes, so that a connection to a node with a lot of links is actually a connection to the ends of many links, said Eriksen.

Looking at the structure this way, and keeping in mind that all link ends have the same probability of being picked, at highly connected nodes links "often get a free ride when a new link is connected to one of the other link ends at the same node," he said.

The researchers used a variation on the random walker diffusion method to detect the modularity of the network from the connected links point of view.

Picture a person exploring a network by walking along its links, said Eriksen. "Whenever the walker comes to a node, he picks at random one of the link ends emanating from that node," he said. If you put many walkers on a network and the walkers make decisions independently of each other, they will eventually reach equilibrium -- if there are twice as many walkers as links, each link will average at any given time two walkers traveling in opposite directions.

The key to uncovering structural traits of the Internet is studying how this ensemble of walkers slowly reaches equilibrium, said Eriksen.

For example, in a network whose patterns resemble North and South America -- with very few links, or roads linking the two parts of the network, or landmasses -- a walker starting in North America and turning left and right at random is not very likely to find the road going to South America, said Eriksen.

"What we observed is that first the walkers within North and South America individually come to an equilibrium... and then later on the number of walkers within each country [reaches] its long-term mean," said Eriksen.

Because the walkers reach an equilibrium in a single area, or module first, the method can be used to detect existing modules of the Internet, and can assess the degree of isolation of an individual module, according to Eriksen.

According to the researchers' simulations, the underlying modular structure of the Internet roughly corresponds to individual countries. "We found that the Internet indeed is modular and we identify the large part of this modularity history in the political and geographical divisions in the real world," said Eriksen. The last place the walkers reached equilibrium, for instance, was between Russia and U.S. military sites, he said. "These are thus the... two parts of the network that are most separated from each other."

To carry out the study, the researchers had to adjust some existing algorithms to develop a practical way to run simulation of many walkers, Eriksen said. "Just... running the simulation of random walkers is not the fastest way to calculate the diffusion modes and identify the modules [and is not] feasible for huge networks," said Eriksen.

They found a way to pose the problem so that the time it took the algorithm to calculate roughly doubled, rather than increasing exponentially, every time the network doubled, he said.

The visual results of the simulations were star-like shapes. Straight lines radiating from the center indicated independent modules.

Traditionally, there are two strategies to determining the modularity of the Internet -- bottom-up or top-down, said Eriksen. The first scenario groups the most similar nodes into a module. The researchers' work falls into the second scenario, which subdivides the network into modules.

Visualizing modularity is a step toward making a coarse-grain description of the Internet that can be used to better understand its architecture and how and where to improve its connectivity, said Eriksen.

The researchers' method could help make Internet topology generators, or simulators, more accurate, according to Eriksen. "We have devised methods to see if the artificial networks generators are capable of this," he added.

As the Internet grows and changes, it is increasingly important to take its basic patterns into consideration, said Eriksen. "When you devise [software like] routing rules for the Internet, you not only want [it] to do well on today's Internet, but also on the Internet of tomorrow, which at the current speed of development might be quite different," he said. "It is... not good if your algorithms only function efficiently due to... special linkage patterns present today but not tomorrow."

Erikson's research colleagues were Ingve Simonsen of the Nordic Institute for Theoretical Physics (NORDITA), Sergei Maslov of the Brookhaven National Laboratory and Kim Sneppen, now at NORDITA. The work appeared in the April 11, 2003 issue of Physical Review Letters. The research was funded by NORDITA, Brookhaven National Laboratory and the Norwegian University of Science and Technology.

Timeline:   Unknown
Funding:   Government
TRN Categories:  Internet; Physics
Story Type:   News
Related Elements:  Technical paper, "Modularity and Extreme Edges of the Internet," posted in the Physics Archive at


July 2/9, 2003

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