Dear Alireza Soroudi

Everything depends on the structure of both - the reliability and/or the energy transfer

(a graph showing how the energy is supplied and then sent between users, etc.).

Moreover, some probabilistic characteristics are required, like rate of failure

of each verices and/or edges, the power sent via each connectio, possibilities of the service and repairs, . . . ) Even simplest models need careful analysis, beginning at the stage of construction of the model, through the calculations or simulations of the evolution of the whole system, especially in the case if some perturbances caused by e.g. destruction appear. Unfortunately, I am familiar only with some elementary examples, which give answer to questions on the reliability of the system. Seemigly the methods can be applied to other features,  for  instance - the asked by you  Expected energy not supplied to/between (?). Frankly, it would be simpler to answer if some detailes about your problem were known :)

Sincerely, Joachim Domsta

PS. Let me suggest  the following  basic book on life testing from the point of view of reliability:Statistical theory of reliability and life testing: probability models

Quoted from internet:

RE Barlow, F Proschan - 1975 - DTIC Document

Abstract: This is the first of two books on the statistical theory of reliability and life testing. The present book concentrates on probabilistic aspects of reliability theory, while the forthcoming book will focus on inferential aspects of reliability and life testing, applying the probabilistic ... JoD

PS2: Also, it is worth to know, that some processes calculating the probability distribution of the total time of staying in chosen states is a strong tool for such problems, see eg.

Maintenance Theory of Reliability, by Toshio Nakagawa

where semiMarkov processes (= Markov renewal processes) are presented with  applications. For an examplary paper on closed problems and methods cf.

http://www.jaqm.ro/issues/volume-5,issue-3/pdfs/grabski.pdf

JoD