  Complex networks can often be decomposed into less complex sub-networks whose
structures can give hints about the functional organization of the network as a
whole. However, these structural motifs can only tell one part of the
functional story because in this analysis each node and edge is treated on an
equal footing. In real networks, two motifs that are topologically identical
but whose nodes perform very different functions will play very different roles
in the network. Here, we combine structural information derived from the
topology of the neuronal network of the nematode C. elegans with information
about the biological function of these nodes, thus coloring nodes by function.
We discover that particular colorations of motifs are significantly more
abundant in the worm brain than expected by chance, and have particular
computational functions that emphasize the feed-forward structure of
information processing in the network, while evading feedback loops.
Interneurons are strongly over-represented among the common motifs, supporting
the notion that these motifs process and transduce the information from the
sensor neurons towards the muscles. Some of the most common motifs identified
in the search for significant colored motifs play a crucial role in the system
of neurons controlling the worm's locomotion. The analysis of complex networks
in terms of colored motifs combines two independent data sets to generate
insight about these networks that cannot be obtained with either data set
alone. The method is general and should allow a decomposition of any complex
network into its functional (rather than topological) motifs as long as both
wiring and functional information is available.
