In this work, we establish theoretical and practical connections between vertex indexing for sparse graph/network compression and matrix ordering for sparse matrix-vector multiplication and variable elimination. We present a fundamental analysis of adjacency access locality in vertex ordering from the perspective of graph composition of, or decomposition into, elementary compact graphs. We introduce an algebraic indexing approach that maintains the advantageous features of existing methods, mitigates their shortcomings, and adapts to the degree distribution. The new method demonstrates superior and versatile performance in graph compression across diverse types of graphs. It also renders proportional improvement in the efficiency of matrix-vector multiplications for subspace iterations in response to random walk queries on a large network.

翻译：在本研究中，我们建立了稀疏图/网络压缩的顶点索引与稀疏矩阵-向量乘法及变量消元的矩阵排序之间的理论和实践联系。我们从图的基本紧凑图组合或分解的角度，对顶点排序中的邻接访问局部性进行了基础性分析。我们提出了一种代数索引方法，该方法保留了现有方法的优势特征，缓解了其缺点，并能适应度分布。新方法在多种类型图的压缩中表现出优越且通用的性能。对于大型网络上的随机游走查询，该方法还能在子空间迭代的矩阵-向量乘法效率上实现成比例的提升。