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Network topology inference is a fundamental problem in many applications of network science, such as locating the source of fake news and brain connectivity network detection. Many real-world situations suffer from a critical problem in which only a limited number of observed nodes are available. In this work, the problem of network topology inference under the framework of partial observability is considered. Based on the vector autoregression model, we propose a novel unbiased estimator for symmetric network topology with Gaussian noise and the Laplacian combination rule. Theoretically, we prove that this estimator converges in probability to the network combination matrix. Furthermore, by utilizing the Gaussian mixture model algorithm, an effective algorithm called the network inference Gauss algorithm is developed to infer the network structure. Finally, compared with state-of-the-art methods, numerical experiments demonstrate that better performance is obtained in the case of small sample sizes when using the proposed algorithm.

An Unbiased Symmetric Matrix Estimator for Topology Inference Under Partial Observability