Internet map improves models

By Kimberly Patch, Technology Research News

As the Internet becomes an increasingly important part of both communications and commerce, it is ever more important to know exactly how it grows.

Scientists from Italy and Spain have analyzed three years worth of daily maps of the Internet's connections in an attempt to better characterize the environment of the real Internet. The study makes a distinction between the Internet, which connects computers around the world in a real network, and software like the Web, which is a virtual network that resides on the Internet.

The researchers used maps of the Internet's connections collected daily by the Cooperative Association for Internet Data Analysis (CAIDA) and the National Laboratory for Applied Network Research (NLANR), which is funded by the U.S. National Science Foundation.

The researchers are looking to closely characterize the Internet because it is an example of a complex network that can be readily analyzed. Their past work was on modeling epidemics and immunization procedures in complex networks like the Internet and networks of human social relationships. "Soon we realized that the deeper analysis, going beyond the simple connectivity properties usually considered, was needed in order to fully characterize the Internet structure," said Romualdo Pastor-Satorras, a visiting professor at the Polytechnic University of Catalonia.

The researchers analyzed Internet growth over time with statistical methods usually used for physics research.

The analysis showed that the Internet grows in specific ways, said Pastor-Satorras. "The Internet can be considered as a spontaneously growing organism. Since there are not global entities regulating the Internet development, it defaults as a self-organized system with high growth rate."

Despite the high growth rate, the Internet has settled into a state whose overall topographical and geometrical properties are stationary in time, said Pastor-Satorras. "The Internet evolved spontaneously [into] a scale-free network characterized by wild fluctuations in the connectivity properties of the [Internet service providers,]" he said. In scale-free networks, a few nodes, or providers, have many connections to other nodes, while many nodes have few connections.

The analysis also showed that nodes, or computers, on the Internet have settled into well-defined, efficient hierarchies that have to do with how the properties of a node are affected by those of its neighbors. "We find that highly connected nodes are more likely connected to nodes with lower connectivity. This allows us to distinguish different layers of the Internet, or small providers connect to larger providers and so on, following a connectivity and size hierarchy," said Pastor-Satorras.

The hierarchy includes stub domains, which are groups of nodes, or computers that carry traffic only within that domain, or group, and transit domains, which connect different stub domains. The connections inside stub domains are usually short, while the connections among domains are usually long. "The existence of stub and transit domains allows us to identify... a hierarchical structure in the Internet," Pastor-Satorras said.

The growth patterns of the Internet show many short interconnections in stub domains but just a few longer links connecting them to each other, which is "quite [economical] in the sense of the total length of the connections established," said Pastor-Satorras.

The information also allows for the study of properties of Internet service providers like "how the connectivity of providers is related to their age, and the death and replacement events occurring in the growth process," he said.

The hierarchy among nodes, the redundant connections that exist among old nodes, and also the real geographical location of nodes can all influence how the Internet evolves, according to Pastor-Satorras.

The information also allowed the researchers to predict the creation of new connections among providers over time. "This gives information on the forces driving the Internet demand and economical market," said Pastor-Satorras.

The information the researchers have gathered can be used to assess the reliability and effectiveness of computer Internet models used to simulate and test new communications protocols and routing algorithms for the Internet, Pastor-Satorras said. It also may prove useful in developing Internet models, he added.

The researchers are working toward more completely mapping the Internet's characteristics, said Pastor-Satorras. "We would like to have a full characterization of the Internet, including the load of information carried on top of the Internet structure. Since we can consider the Internet as a natural object, we would like to pinpoint the dynamical mechanisms driving the Internet formation and provide a quantitative physical model for Internet growth," he said.

The study sheds new light on some aspects of local connectivity, said Bosiljka Tadic, a physics professor at the Jozef Stefan Institute in Slovenia. The researchers found in the data a correlation regarding who connects to whom, he said. "It appears that many nodes with low connectivity are linked to a few nodes with high connectivity, but in a way that cannot be produced in a generic model," he said.

The research is useful for more realistic modeling of the Internet, said Tadic.

The study also showed that the Internet shares many growth factors with the Web, the virtual network that resides on the Internet. "Apart from several important differences [like] link directions, growth of the Internet... and the Web... are guided in part by the same dynamic rules: growth, attachment [and] rewiring," he said.

The work shows how the topological properties of the Internet are determined by the dynamical properties that govern the network's growth, said Albert-László Barabási, a physics professor at the University of Notre Dame. "We are only at the beginning of our understanding of how this topology emerges in real systems," he said.

The work is important because it combines measurements with simulations to shed light on the interplay between topology and growth and paves the way towards realistic network models, Barabási said.

Pastor-Satorras' research colleagues were Alexei Vásquez of the International School for Advanced Studies in Italy and Alessandro Vespignani of the Abdus Salam International Center for Theoretical Physics in Italy. The research was funded by the International Center for Theoretical Physics (ICTP) and the Spanish Ministry of Science and Technology.

Timeline:   Now
Funding:   Government
TRN Categories:   Internet
Story Type:   News
Related Elements:  Technical paper, "Dynamical and Correlation Properties of the Internet," posted on the arXiv physics archive at


April 3/10, 2002

Page One

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