Connectivity, stability and efficiency in a network as an information flow

Abstract We consider the problem of forming a network as an information flow under the requirement that the whole network be connected and remain connected after the destruction of some nodes. We introduce the C q -stability and the C q -efficiency of a network which, roughly speaking, require connectivity in addition to stability and efficiency even after any q nodes are destroyed. We mainly examine the relation between efficiency and stability. With the connectivity requirement, the efficient network is always stable, but the C q -efficient network is not necessarily C q -stable for q ≥ 1. We provide sufficient conditions for a C q -efficient network to be C q -stable.

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