Sommario: | Many complex physical, technological, social, biological and economical systems can be represented in the form of networks, where vertices are the entities of the system and the edges represent the relational links among the entities. Since complex networks display a high degree of tolerance to random failures, errors and attacks, network dependability has always been a challenging task in system reliability analysis. In the literature, network reliability is intended as the probability that two speciﬁc nodes (a source node and a destination node) are connected given the probability of the elements of the network (nodes, edges or both) of being up or down. A number of techniques have been developed to tackle this problem. However, in recent year, with the appearance of networks of giant dimensions (e.g. the internet and www) the exhaustive searching techniques are no more appropriate. A completely new ﬁeld of research has emerged to study the statistical properties of these huge networks, together with the study of their robustness to random failures and attacks. This paper is aimed at illustrating the old a new challenges in network dependability evaluation. |