超越拓扑持久性：从网络开始
Beyond topological persistence: Starting from networks
摘要：
持久同源性使拓扑对象的快速和可计算的比较成为可能。然而，它自然地局限于拓扑空间的分析。我们扩展了持久性理论，通过保证鲁棒性和可计算性的重要数据类型，如单图和颤抖。我们专注于类别持久性功能，使我们能够研究在充分的一般性强的连通性，如集团社区，$k$ -顶点和$k$ -边连通性直接在单图和monic连贯类。
英文摘要：
Persistent homology enables fast and computable comparison of topological objects. However, it is naturally limited to the analysis of topological spaces. We extend the theory of persistence, by guaranteeing robustness and computability to significant data types as simple graphs and quivers. We focus on categorical persistence functions that allow us to study in full generality strong kinds of connectedness such as clique communities, $k$-vertex and $k$-edge connectedness directly on simple graphs and monic coherent categories.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
