我们提出了一种基于复杂网络与持续同调的单变量时间序列分类统一流程。时间序列通过五种图构造方法之一（隶属三类：可见性图（自然可见性图与水平可见性图）、转移图与邻近图）映射为图结构，再将该图转化为非相似性矩阵；由此构建Vietoris-Rips滤链，生成持续同调图（persistence diagrams）。这些图经由持续景观（persistence landscapes）与拓扑摘要统计量向量化为固定长度特征。通过标准化下游处理流程，分类性能差异仅可归因于图构造方式与距离度量的选择。在十二个UCR基准数据集上的实验表明：（i）不存在单一最优构造方式：最优图类型取决于信号的判别性结构；（ii）图距离度量是一阶设计选择，其中扩散距离（diffusion distance）始终优于各类最短路径距离；（iii）基于持续同调的特征在噪声下呈现渐进式性能退化，符合持续同调经典稳定性定理。

We present a unified pipeline for univariate time series classification via complex networks and persistent homology. A time series is mapped to a graph through one of five constructions across three families (visibility (natural and horizontal visibility graphs), transition, and proximity) and the graph is converted to a dissimilarity matrix from which a Vietoris-Rips filtration yields persistence diagrams. These diagrams are vectorized into fixed-length features through persistence landscapes and topological summary statistics. By standardizing the downstream processing, differences in classification performance are attributable to the network construction and distance metric alone. Experiments on twelve UCR benchmarks show that (i) no single construction dominates: the optimal graph type depends on the signal's discriminative structure; (ii) the graph distance metric is a first-order design choice, with diffusion distance uniformly outperforming shortest-path alternatives; and (iii) persistence-based features degrade gracefully under noise, consistent with the classical stability theorem of persistent homology.