Graph is a ubiquitous structure representing entities and their relationships applied in many areas such as social networks, web graphs, and biological networks. One of the fundamental tasks in graph analytics is to investigate the relations between two vertices (e.g., users, items, and entities) such as how a vertex A influences another vertex B, or to what extent A and B are similar to each other, based on the graph topology structure. For this purpose, we study the problem of hop-constrained s-t simple path enumeration in this paper, which aims to list all simple paths from a source vertex s to a target vertex t with hop-constraint k. We first propose a polynomial delay algorithm, namely BC-DFS, based on a barrier-based pruning technique. Then, a join-oriented algorithm, namely JOIN, is designed to further enhance the query response time. On the theoretical side, BC-DFS is a polynomial delay algorithm with O(km) time per output where m is the number of edges in the graph. This time complexity is similar to the best known theoretical result for the polynomial delay algorithms of this problem. On the practical side, our comprehensive experiments on 15 real-life networks demonstrate the superior performance of the BC-DFS algorithm compared to the state-of-the-art techniques. It is also reported that the JOIN algorithm can further significantly enhance the query response time. In this paper, we also study the hop-constrained path enumeration problem with diversity constraint and propose a block-oriented algorithm, namely SCB. To further speed up the computation, hybrid lower bounds based on reverse shortest-path tree are also developed, namely SCB+. The experiments show our proposed methods significantly improve the query time and scalability comparing with baselines.

图是一种普遍存在的结构，表示实体及其在许多领域（如社交网络，网络图和生物网络）中的关系。图分析的基本任务之一是研究两个顶点（例如，用户，项目和实体）之间的关系，例如一个顶点A如何影响另一个顶点B，或者A和B相互之间的相似程度，基于图拓扑结构。为此，我们在本文中研究了跳数受限的s - t简单路径枚举的问题，该问题旨在列出从源顶点s到目标顶点t的所有简单路径。跳数为k。我们首先基于基于障碍的修剪技术提出多项式延迟算法，即BC-DFS。然后，设计了一个面向联接的算法，即JOIN，以进一步延长查询响应时间。从理论上讲，BC-DFS是多项式延迟算法，每个输出的时间为O（km），其中m是图中的边数。此时间复杂度类似于此问题的多项式延迟算法的最著名理论结果。在实践方面，我们在15个现实网络上进行的全面实验证明，与最新技术相比，BC-DFS算法具有卓越的性能。另据报道，JOIN算法可以进一步显着提高查询响应时间。在本文中，我们还研究了具有分集约束的跳约束路径枚举问题，并提出了一种面向块的算法，即SCB。为了进一步加快计算速度，还开发了基于反向最短路径树的混合下界，即SCB +。实验表明，与基线相比，我们提出的方法显着改善了查询时间和可伸缩性。