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The book aims is the studying new class network design problems in undirected graphs, with survivability requirements expressed as connectivity of resulting network with respect to edges failures of a subgraph belonging to certain class. Investigation mathematical models these networks design problems has been stimulated by the practical importance, wide range applications, and new polyhedral results on algorithmic aspects arising from the analysis of some graphic problems studied over the years. Mathematical models of these network design problems arise in transport, physical and biological systems, in sense that the manifested network structures must be stored connectivity after changes in their geometry under the influence of external factors. An important feature of this book is that it comes with software of major algorithms described herein. The book will be useful for researchers, practitioners, and graduate students in operations research, optimization, applied mathematics and computer science. Due to the substantial practical importance of some presented problems, researchers in other areas will find this book useful, too.