  Networks involved in information processing often have their nodes arranged
hierarchically, with the majority of connections occurring in adjacent levels.
However, despite being an intuitively appealing concept, the hierarchical
organization of large networks, such as those in the brain, are difficult to
identify, especially in absence of additional information beyond that provided
by the connectome. In this paper, we propose a framework to uncover the
hierarchical structure of a given network, that identifies the nodes occupying
each level as well as the sequential order of the levels. It involves
optimizing a metric that we use to quantify the extent of hierarchy present in
a network. Applying this measure to various brain networks, ranging from the
nervous system of the nematode Caenorhabditis elegans to the human connectome,
we unexpectedly find that they exhibit a common network architectural motif
intertwining hierarchy and modularity. This suggests that brain networks may
have evolved to simultaneously exploit the functional advantages of these two
types of organizations, viz., relatively independent modules performing
distributed processing in parallel and a hierarchical structure that allows
sequential pooling of these multiple processing streams. An intriguing
possibility is that this property we report may be common to information
processing networks in general.
