Zusammenfassung
As the Internet AS-level topology grows over time, some of its structural
properties remain unchanged. Such time- invariant properties are generally
interesting, because they tend to reflect some fundamental processes or
constraints behind Internet growth. As has been shown before, the
time-invariant structural properties of the Internet include some most basic
ones, such as the degree distribution or clustering. Here we add to this
time-invariant list a non-trivial property - k-dense decomposition. This
property is derived from a recursive form of edge multiplicity, defined as the
number of triangles that share a given edge. We show that after proper
normalization, the k- dense decomposition of the Internet has remained stable
over the last decade, even though the Internet size has approximately doubled,
and so has the k-density of its k-densest core. This core consists mostly of
content providers peering at Internet eXchange Points, and it only loosely
overlaps with the high-degree or high-rank AS core, consisting mostly of tier-1
transit providers. We thus show that high degrees and high k-densities reflect
two different Internet-specific properties of ASes (transit versus content
providers), thus explaining strong fluctuations between degrees and
k-densities, and the related observation that random graphs with the same
degree distribution or even degree correlations as in the Internet, do not
reproduce its k- dense decomposition. Therefore an interesting open question is
what Internet topology models or generators can fully explain or at least
reproduce the k-dense properties of the Internet.
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