The present text was aimed at providing modelling and analysis techniques for the evaluation of reliability measures (2-terminal, all-terminal, k-terminal reliability) for systems whose structure can be described in the form of a probabilistic graph. The techniques described in this text are used to look at networks of tens or hundreds of nodes and could said to be based on the exhaustive search algorithms intended to provide information on the network connectivity, dependability, and vulnerability-qualitatively or quantitatively, and are precursor to furthering the area of network reliability. The challenge is to make such algorithms to cope up with networks of larger dimensions, by exploiting new and more compact data structures and their handing thereof, or even to explore the possibility of approximations (Bounds on network reliability).

Many complex physical, technological, social, biological, and economical systems of today’s real world or even the ubiquitous internet can be represented in the form of a gigantic network graph and can be characterized by a set of nodes connected by directed or undirected arcs. The nodes then represent the entities of the system and the arcs represent the relational links among the entities. The node entities are homogeneous/heterogeneous, static/dynamic, and unpredictable whereas the edges manifolds to be wired/wireless, and fixed/arbitrary. In some networks (e.g., mobile networks), the nodes are constantly in motion and/or operate ...

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