  Driven by growing interest in the sciences, industry, and among the broader
public, a large number of empirical studies have been conducted in recent years
of the structure of networks ranging from the internet and the world wide web
to biological networks and social networks. The data produced by these
experiments are often rich and multimodal, yet at the same time they may
contain substantial measurement error. In practice, this means that the true
network structure can differ greatly from naive estimates made from the raw
data, and hence that conclusions drawn from those naive estimates may be
significantly in error. In this paper we describe a technique that circumvents
this problem and allows us to make optimal estimates of the true structure of
networks in the presence of both richly textured data and significant
measurement uncertainty. We give example applications to two different social
networks, one derived from face-to-face interactions and one from self-reported
friendships.
