  In this paper the web is analyzed as a graph aggregated by host and pay-level
domain (PLD). The web graph datasets, publicly available, have been released by
the Common Crawl Foundation and are based on a web crawl performed during the
period May-June-July 2017. The host graph has $\sim$1.3 billion nodes and
$\sim$5.3 billion arcs. The PLD graph has $\sim$91 million nodes and $\sim$1.1
billion arcs. We study the distributions of degree and sizes of strongly/weakly
connected components (SCC/WCC) focusing on power laws detection using
statistical methods. The statistical plausibility of the power law model is
compared with that of several alternative distributions. While there is no
evidence of power law tails on host level, they emerge on PLD aggregation for
indegree, SCC and WCC size distributions. Finally, we analyze distance-related
features by studying the cumulative distributions of the shortest path lengths,
and give an estimation of the diameters of the graphs.
