This chapter surveys early studies and recent developments in the broad area of analysis and design of robust network clusters with bounded diameter. Low diameter (small number of intermediaries in the shortest path between any two nodes) is a desired property of various infrastructure networks (communication/information exchange, transportation/supply, etc.) However, in addition to low diameter, a network cluster may need to be able to withstand multiple disruptions or failures of their elements (nodes and/or links), which is not always a guaranteed property for networks with low diameter. We review mathematical modeling and optimization aspects of studying network clusters with bounded diameter, including basic models (referred to as k-clique and k-club), as well as generalized models with improved failure/attack tolerance characteristics (i.e., R-robust k-club).
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