  Social networks are rarely observed in full detail. In many situations
properties are known for only a sample of the individuals in the network and it
is desirable to induce global properties of the full social network from this
"egocentric" network data. In the current paper we study a few different types
of egocentric data, and show what global network properties are consistent with
those egocentric data. Two global network properties are considered: the size
of the largest connected component in the network (the giant), and secondly,
the possible size of an epidemic outbreak taking place on the network, in which
transmission occurs only between network neighbours, and with probability $p$.
The main conclusion is that in most cases, egocentric data allow for a large
range of possible sizes of the giant and the outbreak. However, there is an
upper bound for the latter. For the case that the network is selected uniformly
among networks with prescribed egocentric data (satisfying some conditions),
the asymptotic size of the giant and the outbreak is characterised.
