Network embedding (NE) is playing a principal role in network mining, due to its ability to map nodes into efficient low-dimensional embedding vectors. However, two major limitations exist in state-of-the-art NE methods: role preservation and uncertainty modeling. Almost all previous methods represent a node into a point in space and focus on local structural information, i.e., neighborhood information. However, neighborhood information does not capture global structural information and point vector representation fails in modeling the uncertainty of node representations. In this paper, we propose a new NE framework, struc2gauss, which learns node representations in the space of Gaussian distributions and performs network embedding based on global structural information. struc2gauss first employs a given node similarity metric to measure the global structural information, then generates structural context for nodes and finally learns node representations via Gaussian embedding. Different structural similarity measures of networks and energy functions of Gaussian embedding are investigated. Experiments conducted on real-world networks demonstrate that struc2gauss effectively captures global structural information while state-of-the-art network embedding methods fail to, outperforms other methods on the structure-based clustering and classification task and provides more information on uncertainties of node representations.