Comparing complex networks: in defence of the simple

To improve our understanding of connected systems, different tools derived from statistics, signal processing, information theory and statistical physics have been developed in the last decade. Here, we will focus on the graph comparison problem. Although different estimates exist to quantify how different two networks are, an appropriate metric has not been proposed. Within this framework we compare the performances of two networks distances (a topological descriptor and a kernel-based approach as representative methods of the main classes considered) with the simple Euclidean metric. We study the performance of metrics as the efficiency of distinguish two network's groups and the computing time. We evaluate these methods on synthetic and real-world networks (brain connectomes and social networks), and we show that the Euclidean distance efficiently captures networks differences in comparison to other proposals. We conclude that the operational use of complicated methods can be justified only by showing that they outperform well-understood traditional statistics, such as Euclidean metrics.