  We performed a large-scale crawl of the World Wide Web, covering 6.9 Million
domains and 57 Million subdomains, including all high-traffic sites of the
Internet. We present a study of the correlations found between quantities
measuring the structural relevance of each node in the network (the in- and
out-degree, the local clustering coefficient, the first-neighbor in-degree and
the Alexa rank). We find that some of these properties show strong correlation
effects and that the dependencies occurring out of these correlations follow
power laws not only for the averages, but also for the boundaries of the
respective density distributions. In addition, these scale-free limits do not
follow the same exponents as the corresponding averages. In our study we retain
the directionality of the hyperlinks and develop a statistical estimate for the
clustering coefficient of directed graphs.
  We include in our study the correlations between the in-degree and the Alexa
traffic rank, a popular index for the traffic volume, finding non-trivial
power-law correlations. We find that sites with more/less than about one
Thousand links from different domains have remarkably different statistical
properties, for all correlation functions studied, indicating towards an
underlying hierarchical structure of the World Wide Web.
