Network Reliability pp 11-19 | Cite as

# Networks and Examples

## Abstract

This chapter starts with network definition, describes various types of network failure and presents an overview of various network failure criteria. For finite networks, most of these criteria are related to the loss of connectivity between special nodes called terminals. Classical network theory studies infinite network behaviour under node/edge failures, and the main object of interest is the so-called giant component of the network.(see, e.g. [1]) For finite networks, the analogue of it is the largest connected component or a largest cluster in a disintegrating network with failing nodes or edges. We present examples of networks where failure are related to the maximal cluster/component size. The second section is devoted to the simplest network structures–so-called series–parallel and parallel-series networks. We demonstrate that for independently failing elements, reliability analysis of these networks is rather simple.

## Keywords

Network*UP/DOWN*states Terminal connectivity Maximal component Maximal cluster Series/parallel systems

## References

- 1.Newman, M. E. J. (2010).
*Networks: an introduction*. Oxford: Oxford University Press.Google Scholar - 2.Barlow, R. E., & Proschan, F. (1981).
*Statistical theory of reliability and life testing*. To Begin With; Reprint Edition.Google Scholar - 3.Gertsbakh, I. (2000).
*Reliability theory with applications to preventive maintenance*. Berlin: Springer.Google Scholar - 4.Gertsbakh, I., & Shpungin, Y. (2009).
*Models of network reliability: analysis, combinatorics and Monte Carlo*. Boca Raton: CRC Press.Google Scholar - 5.Gertsbakh, I., & Shpungin, Y. (2011).
*Network reliability and resilience*. Berlin: Springer.Google Scholar