  Given a network, we would like to determine which subset of nodes should be
measured by limited sensing facilities to maximize information about the entire
network. The optimal choice corresponds to the configuration that returns the
highest value of a measure of observability of the system. Here, the
determinant of the inverse of the observability Gramian is used to evaluate the
degree of observability. Additionally, the effects of changes in the topology
of the corresponding graph of a network on the observability of the network are
investigated. The theory is illustrated on the problem of detection of an
epidemic disease in a community. The purpose here is to find the smallest
number of people who must be examined to predict the number of infected people
in an arbitrary community. Results are demonstrated in simulation.
