The practical utility of a quantum network depends on its ability to establish entanglement between arbitrary node pairs with quality sufficient to execute entanglement-enabled tasks. This capability can be assessed globally, through aggregate performance over all node pairs, as well as locally, at the level of individual nodes. Since entanglement-based connections define a functional layer above the underlying physical topology, classical connectivity measures alone are insufficient to characterize quantum networks. To enable characterisation of the quantum connectivity at the level of the network (or its subnetworks), we introduce the quantum connectivity measure (QCM), which quantifies the average connection quality between pairs of network nodes. We further define two quantities derived from the QCM: the quantum-connected fraction (QCF) and the quantum clustering coefficient (QCC), which capture important features of the functional connectivity of the quantum network at the level of the network and an individual node, respectively. These metrics depend on the entanglement distribution protocol as well as the network parameters, and therefore capture functional aspects of quantum connectivity beyond physical topology alone. We validate the proposed measures on random and fully connected network topologies, demonstrating, in particular, that a physically fully connected graph can become functionally disconnected for quantum tasks when the average network edge concurrence falls below a critical threshold. These metrics provide useful tools for the design, optimization, and benchmarking of future quantum networks.