Abstract: In this paper, we employ a directed hypergraph model
to investigate the extent to which environmental variability influences
the set of available biochemical reactions within a living cell.
Such an approach avoids the limitations of the usual complex
network formalism by allowing for the multilateral relationships (i.e.
connections involving more than two nodes) that naturally occur
within many biological processes. More specifically, we extend the
concept of network reciprocity to complex hyper-networks, thus
enabling us to characterise a network in terms of the existence
of mutual hyper-connections, which may be considered a proxy
for metabolic network complexity. To demonstrate these ideas, we
study 115 metabolic hyper-networks of bacteria, each of which
can be classified into one of 6 increasingly varied habitats.
In particular, we found that reciprocity increases significantly
with increased environmental variability, supporting the view that
organism adaptability leads to increased complexities in the resultant
biochemical networks.