Here, we presume that there is some valuable information encoded in the network; the problem is simply to find it. One approach for doing so is to draw a full diagram of the network, since this can, if clearly drawn, contain all of the recorded information. However, an unambiguous diagram is only feasible for very small networks, in which case it is unlikely that the mathematical abstraction will return any surprising results. To learn about a network of any significant size it is therefore necessary to characterise it by summary descriptions, which we will refer to as metrics.

We introduce a more systematic framework, in the form of a matrix whose rows correspond to networks, and columns to metrics; we term this the data matrix. Each element of the data matrix contains the value of one metric as applied to one network. In this paper we show that this framework enables the systematic comparison of networks and metrics, and demonstrate its utility in the objective selection of metrics for a given purpose; in model fitting; in the analysis of evolving networks; and to determine the robustness of metrics to variations in network size, network damage and sampling effects.