How can we decipher the hidden structure of a network based on limited observations? This question arises in many scenarios ranging from social to wireless and to neural networks. In such settings, we typically observe the nodes’ behaviors (e.g., the time a node learns about a piece of information, or the time a node gets infected by a disease), and we are interested in inferring the true network over which the diffusion takes place. In this paper, we consider this problem over a neural network where our aim is to reconstruct the connectivity between neurons merely by observing their firing activity. We develop an iterative NEUral INFerence algorithm NEUINF to identify the type of effective neural connections (i.e. excitatory/inhibitory) based on the Perceptron learning rule. We provide theoretical bounds on the average performance of NEUINF as well as numerical analysis to compare the performance of the proposed approach to some previous art.