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We present suitable design patterns and basic algorithms and use them to discuss the computation of popular network indices. With methods from discrete statistics, we are able to visualize and summarize these results for large networks. Furthermore, we talk about heuristic speed-up and approximation techniques to handle even networks that are too large to get the correct results in an acceptable time.

One goal in network design is the construction of sparse networks that guarantee short distances with respect to some given distance requirements. By this, it can be guaranteed, for example, that delays that are incurred by link faults are bounded. An appropriate graph-theoretic model for this is the concept of k-spanners: Given a graph G, a k-spanner of G is a spanning subgraph S, such that the distance between any two vertices in S is at most k times longer than the distance in G. Research in this area has mainly concentrated on two aspects: minimum k-spanners, i.e., k-spanners that contain the fewest edges among all k-spanners, and tree k-spanners, i.e., spanners that are trees. In this thesis, we use k-spanners to model further desirable properties from network design (such as reliability) within a graph-theoretic framework. Our main emphasis is on sparse graphs that guarantee short distances, and we are interested in simple structures and fault-tolerance.