  Much recent research has dealt with the identifiability of a dynamical
network in which the node signals are connected by causal linear transfer
functions and are excited by known external excitation signals and/or unknown
noise signals. A major research question concerns the identifiability of the
whole network - topology and all transfer functions - from the measured node
signals and external excitation signals. So far all results on this topic have
assumed that all node signals are measured. This paper presents the first
results for the situation where not all node signals are measurable, under the
assumptions that (1) the topology of the network is known, and (2) each node is
excited by a known external excitation. Using graph theoretical properties, we
show that the transfer functions that can be identified depend essentially on
the topology of the paths linking the corresponding vertices to the measured
nodes. A practical outcome is that, under those assumptions, a network can
often be identified using only a small subset of node measurements.
