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We present a new, novel approach to obtaining a network's connectivity. Morespecifically, we show that there exists a relationship between a network'sgraph isoperimetric properties and its conditional connectivity. A network'sconnectivity is the minimum number of nodes, whose removal will cause thenetwork disconnected. It is a basic and important measure for the network'sreliability, hence its overall robustness. Several conditional connectivitieshave been proposed in the past for the purpose of accurately reflecting variousrealistic network situations, with extra connectivity being one suchconditional connectivity. In this paper, we will use isoperimetric propertiesof the hypercube network to obtain its extra connectivity. The result of thepaper for the first time establishes a relationship between the age-oldisoperimetric problem and network connectivity.

From Graph Isoperimetric Inequality to Network Connectivity -- A New Approach