  Given any complex directed network, a set of acyclic subgraphs - the
hierarchical backbone of the network - can be extracted that will provide
valuable information about its hierarchical structure. The current paper
presents how the interpretation of the network weight matrix as a transition
matrix allows the hierarchical backbone to be identified and characterized in
terms of the concepts of hierarchical degree, which expresses the total number
of virtual edges established along successive transitions, and of hierarchical
successors, namely the number of nodes accessible from a specific node while
moving successive hierarchical levels. The potential of the proposed approach
is illustrated with respect to word associations and gene sequencing data.
