When analyzing a visualized network, users need to explore different sections of the network to gain insight. However, effective exploration of large networks is often a challenge. While various tools are available for users to explore the global and local features of a network, these tools usually require significant interaction activities, such as repetitive navigation actions to follow network nodes and edges. In this paper, we propose a structure-based suggestive exploration approach to support effective exploration of large networks by suggesting appropriate structures upon user request. Encoding nodes with vectorized representations by transforming information of surrounding structures of nodes into a high dimensional space, our approach can identify similar structures within a large network, enable user interaction with multiple similar structures simultaneously, and guide the exploration of unexplored structures. We develop a web-based visual exploration system to incorporate this suggestive exploration approach and compare performances of our approach under different vectorizing methods and networks. We also present the usability and effectiveness of our approach through a controlled user study with two datasets.