Centrality descriptors are widely used to rank nodes according to specific
concept(s) of importance. Despite the large number of centrality measures
available nowadays, it is still poorly understood how to identify the node
which can be considered as the `centre' of a complex network...
In fact, this
problem corresponds to finding the median of a complex network. The median is a
non-parametric and robust estimator of the location parameter of a probability
distribution. In this work, we present the most natural generalisation of the
concept of median to the realm of complex networks, discussing its advantages
for defining the centre of the system and percentiles around that centre. To
this aim, we introduce a new statistical data depth and we apply it to networks
embedded in a geometric space induced by different metrics. The application of
our framework to empirical networks allows us to identify median nodes which
are socially or biologically relevant.