  Networks are fundamental for our understanding of complex systems.
Interactions between individual nodes in networks generate network motifs -
small recurrent patterns that can be considered the network's building-block
components, providing certain dynamical properties. However, it remains unclear
how network motifs are arranged within networks and what properties emerge from
interactions between network motifs. Here we develop a framework to explore the
mesoscale-level behavior of complex networks. Considering network motifs as
hyper-nodes, we define the rules for their interaction at the network's next
level of organization. We infer the favorable arrangements of interactions
between network motifs into hyper-motifs from real evolved and designed
networks data including biological, neuronal, social, linguistic and electronic
networks. We mathematically explore the emergent properties of these
higher-order circuits and their relations to the properties of the individual
minimal circuit components they combine. This framework provides a basis for
exploring the mesoscale structure and behavior of complex systems where it can
be used to reveal intermediate patterns in complex networks and to identify
specific nodes and links in the network that are the key drivers of the
network's emergent properties.
