Machine learning on graph data has gained sig-nificant interest because of its applicability to various domainsranging from product recommendations to drug discovery. Whilethere is a rapid growth in the algorithmic community, the com-puter architecture community has so far focused on a subset ofgraph learning algorithms including Graph Convolution Network(GCN), and a few others. In this paper, we study another, morescalable, graph learning algorithm based onrandom walks, whichoperates on dynamic input graphs and has attracted less attentionin the architecture community compared to GCN. We proposehigh-performance CPU and GPU implementations of two keygraph learning tasks, that cover a broad class of applications,using random walks on continuous-time dynamic graphs: linkprediction and node classification. We show that the resultingworkload exhibits distinct characteristics, measured in terms ofirregularity, core and memory utilization, and cache hit rates,compared to graph traversals, deep learning, and GCN. Wefurther conduct an in-depth performance analysis focused onboth algorithm and hardware to guide future software optimiza-tion and architecture exploration. The algorithm-focused studypresents a rich trade-off space between algorithmic performanceand runtime complexity to identify optimization opportunities.We find an optimal hyperparameter setting that strikes balancein this trade-off space. Using this setting, we also perform adetailed microarchitectural characterization to analyze hardwarebehavior of these applications and uncover execution bottlenecks,which include high cache misses and dependency-related stalls.The outcome of our study includes recommendations for furtherperformance optimization, and open-source implementations forfuture investigation.