  In this study, we propose an algorithm for computing the network size of
communicating agents. The algorithm is distributed: a) it does not require a
leader selection; b) it only requires local exchange of information, and; c)
its design can be implemented using local information only, without any global
information about the network. It is privacy-preserving, namely it does not
require to propagate identifying labels. This algorithm is based on system
identification, and more precisely on the identification of the order of a
suitably-constructed discrete-time linear time-invariant system over some
finite field. We provide a probabilistic guarantee for any randomly picked node
to correctly compute the number of nodes in the network. Moreover, numerical
implementation has been taken into account to make the algorithm applicable to
networks of hundreds of nodes, and therefore make the algorithm applicable in
real-world sensor or robotic networks. We finally illustrate our results in
simulation and conclude the paper with discussions on how our technique differs
from a previously-known strategy based on statistical inference.
