Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-16T08:18:01.657Z Has data issue: false hasContentIssue false

Expected Value Expansions in Random Subgraphs with Applications to Network Reliability

Published online by Cambridge University Press:  01 December 1998

University of Alabama in Huntsville, Huntsville, AL 35899, USA (e-mail:


Subgraph expansions are commonly used in the analysis of reliability measures of a failure-prone graph. We show that these expansions are special cases of a general result on the expected value of a random variable defined on a partially ordered set; when applied to random subgraphs, the general result defines a natural association between graph functions. As applications, we consider several graph invariants that measure the connectivity of a graph: the number of connected vertex sets of size k, the number of components of size k, and the total number of components. The expected values of these invariants on a random subgraph are global performance measures that generalize the ones commonly studied. Explicit results are obtained for trees, cycles, and complete graphs. Graphs which optimize these performance measures over a given class of graphs are studied

Research Article
1998 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)