Graph representation learning seeks to transform complex, high-dimensional graph structures into compact vector spaces that preserve both topology and semantics. Among the various strategies, subgraph-based methods provide an interpretable bridge between symbolic pattern discovery and continuous embedding learning. Yet, existing frequent or discriminative subgraph mining approaches often suffer from redundant multi-phase pipelines, high computational cost, and weak coupling between mined structures and their discriminative relevance. We propose DS-Span, a single-phase discriminative subgraph mining framework that unifies pattern growth, pruning, and supervision-driven scoring within one traversal of the search space. DS-Span introduces a coverage-capped eligibility mechanism that dynamically limits exploration once a graph is sufficiently represented, and an information-gain-guided selection that promotes subgraphs with strong class-separating ability while minimizing redundancy. The resulting subgraph set serves as an efficient, interpretable basis for downstream graph embedding and classification. Extensive experiments across benchmarks demonstrate that DS-Span generates more compact and discriminative subgraph features than prior multi-stage methods, achieving higher or comparable accuracy with significantly reduced runtime. These results highlight the potential of unified, single-phase discriminative mining as a foundation for scalable and interpretable graph representation learning.