In this paper, we propose a next-generation link prediction method, Weisfeiler-Lehman Neural Machine (WLNM), which learns topological features in the form of graph patterns that promote the formation of links. WLNM has unmatched advantages including higher performance than state-of-the-art methods and universal applicability over various kinds of networks. WLNM extracts an enclosing subgraph of each target link and encodes the subgraph as an adjacency matrix. The key novelty of the encoding comes from a fast hashing-based Weisfeiler-Lehman (WL) algorithm that labels the vertices according to their structural roles in the subgraph while preserving the subgraph's intrinsic directionality. After that, a neural network is trained on these adjacency matrices to learn a predictive model. Compared with traditional link prediction methods, WLNM does not assume a particular link formation mechanism (such as common neighbors), but learns this mechanism from the graph itself. We conduct comprehensive experiments to show that WLNM not only outperforms a great number of state-of-the-art link prediction methods, but also consistently performs well across networks with different characteristics.