The dynamics and function of a network are influenced by the topology of the network. A great need exists for the development of effective methods of inferring network structure. In the past few years, topology identification of complex networks has received intensive interest and quite a few works have been published in literature. However, in most of the publications, each state of a multidimensional node in the network has to be observable, and usually the nodal dynamics is assumed known. In this paper, a new method of recovering the underlying directed connections of a network from the observation of only one state of each node is proposed. The validity of the proposed approach is illustrated with a coupled FitzHugh-Nagumo neurobiological network by only observing the membrane potential of each neuron and found to outperform the traditional Granger causality method. The network coupling strength and noise intensity which might also affect the effectiveness of our method are further analyzed.