  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 different networks distances (a
topological descriptor and a kernel-based approach) with the simple Euclidean
metric. We define the performance of metrics as the efficiency of distinguish
two network's groups and the computing time. We evaluate these frameworks on
synthetic and real-world networks (functional connectomes from Alzheimer
patients and healthy subjects), and we show that the Euclidean distance is the
one that 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 out-perform well-understood traditional
statistics, such as Euclidean metrics.
