  Traditional methods for the analysis of compositional data consider the
log-ratios between all different pairs of variables with equal weight,
typically in the form of aggregated contributions. This is not meaningful in
contexts where it is known that a relationship only exists between very
specific variables (e.g.~for metabolomic pathways), while for other pairs a
relationship does not exist. Modeling absence or presence of relationships is
done in graph theory, where the vertices represent the variables, and the
connections refer to relations. This paper links compositional data analysis
with graph signal processing, and it extends the Aitchison geometry to a
setting where only selected log-ratios can be considered. The presented
framework retains the desirable properties of scale invariance and
compositional coherence. An additional extension to include absolute
information is readily made. Examples from bioinformatics and geochemistry
underline the usefulness of thisapproach in comparison to standard methods for
compositional data analysis.
