  We introduce the graphlet decomposition of a weighted network, which encodes
a notion of social information based on social structure. We develop a scalable
inference algorithm, which combines EM with Bron-Kerbosch in a novel fashion,
for estimating the parameters of the model underlying graphlets using one
network sample. We explore some theoretical properties of the graphlet
decomposition, including computational complexity, redundancy and expected
accuracy. We demonstrate graphlets on synthetic and real data. We analyze
messaging patterns on Facebook and criminal associations in the 19th century.
