Graph Convolutional Networks (GCNs) have long set the state-of-the-art in skeleton-based action recognition, leveraging their ability to unravel the complex dynamics of human joint topology through the graph’s adjacency matrix. However, an inherent flaw has come to light in these cutting-edge models: they tend to optimize the adjacency matrix jointly with the model weights. This process, while seemingly efficient, causes a gradual decay of bone connectivity data, resulting in a model indifferent to the very topology it sought to represent. To remedy this, we propose a two-fold strategy: (1) We forge an innovative approach that encodes bone connectivity by harnessing the power of graph distances to describe the physical topology; we further incorporate action-specific topological representation via persistent homology analysis to depict systemic dynamics. This preserves the vital topological nuances often lost in conventional GCNs. (2) Our investigation also reveals the redundancy in existing GCNs for multi-relational modeling, which we address by proposing an efficient refinement to Graph Convolutions (GC) - the BlockGC. This significantly reduces parameters while improving performance beyond original GCNs. Our full model, the BlockGCN, establishes new benchmarks in skeleton-based action recognition across all model categories. Its high accuracy and lightweight design, most notably on the large-scale NTU RGB+D 120 dataset, stand as strong validation of the efficacy of BlockGCN.