  Biological and technological networks contain patterns, termed network
motifs, which occur far more often than in randomized networks. Network motifs
were suggested to be elementary building blocks that carry out key functions in
the network. It is of interest to understand how network motifs combine to form
larger structures. To address this, we present a systematic approach to define
'motif generalizations': families of motifs of different sizes that share a
common architectural theme. To define motif generalizations, we first define
'roles' in a subgraph according to structural equivalence. For example, the
feedforward loop triad, a motif in transcription, neuronal and some electronic
networks, has three roles, an input node, an output node and an internal node.
The roles are used to define possible generalizations of the motif. The
feedforward loop can have three simple generalizations, based on replicating
each of the three roles and their connections. We present algorithms for
efficiently detecting motif generalizations. We find that the transcription
networks of bacteria and yeast display only one of the three generalizations,
the multi-output feedforward generalization. In contrast, the neuronal network
of \emph{C. elegans} mainly displays the multi-input generalization.
Forward-logic electronic circuits display a multi-input, multi-output hybrid.
Thus, networks which share a common motif can have very different
generalizations of that motif. Using mathematical modelling, we describe the
information processing functions of the different motif generalizations in
transcription, neuronal and electronic networks.
