Abstract
Abstract We study complex networks in which the nodes
are tagged with different colors depending on their
function (colored graphs), using information theory
applied to the distribution of motifs in such networks.
We find that colored motifs can be viewed as the
building blocks of the networks (much more than the
uncolored structural motifs can be) and that the
relative frequency with which these motifs appear in
the network can be used to define its information
content. This information is defined in such a way that
a network with random coloration (but keeping the
relative number of nodes with different colors the
same) has zero color information content. Thus, colored
motif information captures the exceptionality of
coloring in the motifs that is maintained via
selection. We study the motif information content of
the C. elegans brain as well as the evolution of
colored motif information in networks that reflect the
interaction between instructions in genomes of digital
life organisms. While we find that colored motif
information appears to capture essential functionality
in the C. elegans brain (where the color assignment of
nodes is straightforward), it is not obvious whether
the colored motif information content always increases
during evolution, as would be expected from a measure
that captures network complexity. For a single choice
of color assignment of instructions in the digital life
form Avida, we find rather that colored motif
information content increases or decreases during
evolution, depending on how the genomes are organized,
and therefore could be an interesting tool to dissect
genomic rearrangements.
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