In complex networks a common task is to identify the most important or “central” nodes. There are several definitions, often called centrality measures, which often lead to different results. Here, we introduce fingerprints of networks, which we define as correlation plots of local and global network properties. We show that these fingerprints are suitable tools for characterizing networks beyond single-quantity distributions. In particular, we study the correlations between four local and global measures, namely the degree, the shortest-path betweenness, the random-walk betweenness and the subgraph centrality on different random-network models like Erdős–Rényi, small-world and Barabási–Albert as well as on different real networks like metabolic pathways, social collaborations and computer networks and compare those fingerprints to determine the quality of those basic models. The correlation fingerprints are quite different between the real networks and the model networks questioning whether the models really reflect all important properties of the real world.