  We study the structure of the social graph of active Facebook users, the
largest social network ever analyzed. We compute numerous features of the graph
including the number of users and friendships, the degree distribution, path
lengths, clustering, and mixing patterns. Our results center around three main
observations. First, we characterize the global structure of the graph,
determining that the social network is nearly fully connected, with 99.91% of
individuals belonging to a single large connected component, and we confirm the
"six degrees of separation" phenomenon on a global scale. Second, by studying
the average local clustering coefficient and degeneracy of graph neighborhoods,
we show that while the Facebook graph as a whole is clearly sparse, the graph
neighborhoods of users contain surprisingly dense structure. Third, we
characterize the assortativity patterns present in the graph by studying the
basic demographic and network properties of users. We observe clear degree
assortativity and characterize the extent to which "your friends have more
friends than you". Furthermore, we observe a strong effect of age on friendship
preferences as well as a globally modular community structure driven by
nationality, but we do not find any strong gender homophily. We compare our
results with those from smaller social networks and find mostly, but not
entirely, agreement on common structural network characteristics.
