Internet Connectivity: Disassortative and Assortative Behavior

Title: Internet Connectivity: Disassortative and Assortative Behavior

Authors: Shi Zhou & Raul J. Mondragon

Research Question: How does the Internet's connectivity between high-degree nodes behave? Is it disassortative or assortative?

Methodology: The researchers divided the network nodes into subsets based on their ranks. They measured the subset-subset link distribution, which is the joint probability distribution that a link connects members of the same subset or different subsets. They used a 3D histogram to illustrate this distribution, with nodes divided into 5% node rank bins.

Results: The researchers found that the AS-level Internet shows both disassortative and assortative mixing. Disassortative mixing refers to low-degree subsets connecting to high-degree subsets, while assortative mixing refers to a higher probability of links connecting members inside the high-degree subset. They also measured the rich-club connectivity (rϕ), which is the ratio of the actual number of links to the maximum possible number of links between nodes with rank less than r. They found that high-degree nodes in the AS-level Internet are significantly better connected with each other than those in the BA network.

Implications: The researchers' findings suggest that the AS-level Internet's heterogeneous mixing property is coherent with its evolution. Newly added nodes tend to connect to high-degree nodes, and high-degree nodes acquire new links to improve their routing performance. This behavior is reflected in the disassortative and assortative mixing observed in the network. The researchers' results also imply that the Interactive Growth (IG) model, which adopts assortative behavior, can generate networks that closely match the AS-level Internet's connectivity characteristics.

Link to Article: https://arxiv.org/abs/0308036v1 Authors: arXiv ID: 0308036v1