We show that the average of the maximum teleportation fidelities between all pairs of nodes in a large quantum repeater network is a measure of the resourcefulness of the network as a whole. It can be used to rank networks of arbitrary topologies, with and without loops. For demonstration purposes, we use simple Werner state-based models to characterize some fundamental topologies (the star, the chain, some trees, and also the ring and the complete graph) with this measure in three (semi)realistic scenarios. Most of our results are analytic and apply to arbitrary network sizes. We identify the parameter ranges where these networks can achieve quantum advantages and show the large-$N$ behaviors.

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• Quantum networks
• Quantum repeaters