  Nodes in networks that exhibit high connectivity, also called ``hubs'', play
a critical role in determining the structural and functional properties of
networked systems. However, there is no clear definition of what constitutes a
hub node in a network, and the classification of network hubs in existing work
has either been purely qualitative or relies on ad hoc criteria for
thresholding continuous data that do not generalize well to networks with
certain degree sequences. Here we develop a set of efficient nonparametric
methods that classify hub nodes in directed networks using the Minimum
Description Length principle, effectively providing a clear and principled
definition for network hubs. We adapt our methods to both unweighted and
weighted networks and demonstrate them in a range of example applications using
real and synthetic network data.
