The success of many graph-based machine learning tasks highly depends on an appropriate representation learned from the graph data. Most work has focused on learning node embeddings that preserve proximity as opposed to structural role-based embeddings that preserve the structural similarity among nodes. These methods fail to capture higher-order structural dependencies and connectivity patterns that are crucial for structural role-based applications such as visitor stitching from web logs. In this work, we formulate higher-order network representation learning and describe a general framework called HONE for learning such structural node embeddings from networks via the subgraph patterns (network motifs, graphlet orbits/positions) in a nodes neighborhood. A general diffusion mechanism is introduced in HONE along with a space-efficient approach that avoids explicit construction of the k-step motif-based matrices using a k-step linear operator. Furthermore, HONE is shown to be fast and efficient with a worst-case time complexity that is nearly-linear in the number of edges. The experiments demonstrate the effectiveness of HONE for a number of important tasks including link prediction and visitor stitching from large web log data.