The applications of networks can be observed in numerous engineering realms mainly computers and communication, transportation, electric transmission and oil and gas distribution. Estimating the reliability of such networks is a critical task for the well-being of society as well as a nation. The paradigm of network reliability has evolved considerably over the past few decades. The purpose of this article is to present the developments in network reliability domain in a laconic manner. This paper discusses the various metrics used to evaluate network connectivity along with their mathematical backgrounds. The various algorithms namely State Enumeration, Sum of disjoint product, Minimal Cut Set, Factoring theorem, Cellular Automata, Subset Simulation, Percolation theory, Binary Decision Diagrams, and Universal Generating Functions are enumerated in this review study. The application part of algorithms with their advantages, limitations and scope are presented. Finally, the methodologies used for assessment of network reliability are discussed. This article aims at providing a holistic view of the network reliability practices, which may prove to be helpful for researchers across the globe.

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