用双随机矩阵替代传统图卷积中的拉普拉斯矩阵，提升多跳邻近与局部中心性建模。

Graph Neural Networks (GNNs) conventionally rely on standard Laplacian or adjacency matrices for structural message passing. In this work, we substitute the traditional Laplacian with a Doubly Stochastic graph Matrix (DSM), derived from the inverse of the modified Laplacian, to naturally encode continuous multi-hop proximity and strict local centrality. To overcome the intractable $O(n^3)$ complexity of exact matrix inversion, we first utilize a truncated Neumann series to scalably approximate the DSM, which serves as the foundation for our proposed DsmNet. Furthermore, because algebraic truncation inherently causes probability mass leakage, we introduce DsmNet-compensate. This variant features a mathematically rigorous Residual Mass Compensation mechanism that analytically re-injects the truncated tail mass into self-loops, strictly restoring row-stochasticity and structural dominance. Extensive theoretical and empirical analyses demonstrate that our decoupled architectures operate efficiently in $O(K|E|)$ time and effectively mitigate over-smoothing by bounding Dirichlet energy decay, providing robust empirical validation on homophilic benchmarks. Finally, we establish the theoretical boundaries of the DSM on heterophilic topologies and demonstrate its versatility as a continuous structural encoding for Graph Transformers.