A global measure of network connectivity

Abstract

Network topologies for large computer networks must be resistant to multiple failures. Previously proposed metrics for fault tolerance in this respect (such as connectivity) measure the difficulty of disconnecting any portion of the network from the remainder. The separation of a single processor or even a small set of processors by a small number of failures is often not very significant. However, a small number of failures should not disconnect a large part of the network. We present a new metric, called the connectivity function, that allows this kind of consideration to be assessed. A topology's connectivity function describes the difficulty of separating significant parts of the network. We present results on the properties of the connectivity function and show how it can be used to characterize the fault tolerant properties of some common static network topologies.