  We derive conditions for the identifiability of nonlinear networks
characterized by additive dynamics at the level of the edges when all the nodes
are excited. In contrast to linear systems, we show that the measurement of all
sinks is necessary and sufficient for the identifiability of directed acyclic
graphs, under the assumption that dynamics are described by analytic functions
without constant terms (i.e., $f(0)=0$). But if constant terms are present,
then the identifiability is impossible as soon as one node has more than one
in-neighbor. In the case of general digraphs where cycles can exist, we
consider additively separable functions for the analysis of the
identifiability, and we show that the measurement of one node of all the sinks
of the condensation digraph is necessary and sufficient. Several examples are
added to illustrate the results.
