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