  The analysis of small recurrent substructures, so called network motifs, has
become a standard tool of complex network science to unveil the design
principles underlying the structure of empirical networks. In many natural
systems network nodes are associated with an intrinsic property according to
which they can be ordered and compared against each other. Here, we expand
standard motif analysis to be able to capture the hierarchical structure in
such ordered networks. Our new approach is based on the identification of all
ordered 3-node substructures and the visualization of their significance
profile. We present a technique to calculate the fine grained motif spectrum by
resolving the individual members of isomorphism classes (sets of substructures
formed by permuting node-order). We apply this technique to computer generated
ensembles of ordered networks and to empirical food web data, demonstrating the
importance of considering node order for food-web analysis. Our approach may
not only be helpful to identify hierarchical patterns in empirical food webs
and other natural networks, it may also provide the base for extending motif
analysis to other types of multi-layered networks.
