Keywords: networks, survivability, resilience, computational complexity.

In the past, the ability of engineering networks (e.g. electric power, gas, water, transportation systems) to withstand massive sudden damage caused by adverse events (or survivability) has not been included within design goals. Modern networks, however, are more vulnerable to such events and their failure can have unprecedented effect on lives and economy.

To mitigate the consequences of adverse events, mathematical and computational tools are required to evaluate the survivability of existing networks, analyse the efficiency of different design strategies for enhancing the network survivability, and compare the survivability of alternative designs for future networks.

This paper is concerned with the impact of the network's topology on its survivability. The network's topology is defined as the number of network components, their type, and how the network components are connected to one another. Network analysis is the most suitable framework for such a problem.

Engineering networks fall into the category of large-scale networks with heterogeneous nodes such as sources and sinks. In such networks, survivability is perceived as the continuation of a supply of a quality of interest (service) from sources to sinks in the amount sufficient to satisfy their demand in the presence of multiple faults in network elements. Depending on the origin and evolution of faults, the amount of a quality of interest available to each sink may vary with time. Intuitively, however, the word "survivability" is associated not with a process, but with a final state of a system after all possible damage has occurred and before any recovery action can take place. This is an approach adopted in this study.

The survivability analysis of networks with heterogeneous nodes requires the analysis of the connectivity of the network components for every possible combination of faults to determine a network response to each combination of faults. From the computational complexity point of view, the problem belongs to the class of exponential time problems at least. As the authors showed previously, the problem complexity can partially be reduced by mapping the initial topology of a complex large-scale network with multiple sources and multiple sinks onto a set of smaller sub-topologies with multiple sources and a single sink connected to the network of sources by a single link. In this paper, the mapping procedure is applied to the Florida power grid.

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