  We study here the clustering of directed social graphs. The clustering
coefficient has been introduced to capture the social phenomena that a friend
of a friend tends to be my friend. This metric has been widely studied and has
shown to be of great interest to describe the characteristics of a social
graph. In fact, the clustering coefficient is adapted for a graph in which the
links are undirected, such as friendship links (Facebook) or professional links
(LinkedIn). For a graph in which links are directed from a source of
information to a consumer of information, it is no more adequate. We show that
former studies have missed much of the information contained in the directed
part of such graphs. We thus introduce a new metric to measure the clustering
of a directed social graph with interest links, namely the interest clustering
coefficient. We compute it (exactly and using sampling methods) on a very large
social graph, a Twitter snapshot with 505 million users and 23 billion links.
We additionally provide the values of the formerly introduced directed and
undirected metrics, a first on such a large snapshot. We exhibit that the
interest clustering coefficient is larger than classic directed clustering
coefficients introduced in the literature. This shows the relevancy of the
metric to capture the informational aspects of directed graphs.
