A variety of probabilistic notions of network reliability of graphs and digraphs have been proposed and studied since the early 1950s. Although grounded in the engineering and logistics of network design and analysis, the research also spans pure and applied mathematics, with connections to areas as diverse as combinatorics and graph theory, combinatorial enumeration, optimization, probability theory, real and complex analysis, algebraic topology, commutative algebra, the design and analysis of algorithms, and computational complexity. In this paper we describe the landscape of various notions of network reliability, the roads well traveled, and some that appear likely to lead to meaningful and important journeys.

中文翻译：

---

网络可靠性：在高速公路上前进

自1950年代初以来，已经提出并研究了多种图和有向图网络可靠性的概率概念。尽管以网络设计和分析的工程和物流为基础，但该研究还涉及纯数学和应用数学，涉及范围广泛，包括组合论和图论，组合枚举，优化，概率论，实数和复杂分析，代数拓扑，交换代数，算法的设计和分析以及计算复杂性。在本文中，我们描述了各种网络可靠性概念的概况，通行的道路以及一些可能导致有意义且重要的旅程的道路。