  An ecological network is a formal representation of a specific type of
interaction in a corresponding ecosystem. Such networks have traditionally been
modelled as encoding exclusively pairwise interactions among the fundamental
units of ecosystems and have been represented and analysed using
graph-theoretic methods. However, many real-world ecosystems may entertain
non-binary, polyadic relations between their units, which cannot be captured by
the pairwise interaction methods, but require higher-order interaction
framework, and consequently the corresponding ecological networks cannot be
modelled using graph-theoretic framework. This work gives a structural
definition of ecological network suitable for modelling all orders of
interactions between the fundamental units of the corresponding ecological
system, including and going beyond the pairwise interaction framework. Carbon
mediation between units of some select ecosystems are studied by modelling the
corresponding ecological networks as simplicial complexes following the
definition. The concept of graph centrality measure has been extended to
simplicial centrality, and some important centrality measures of these networks
at various structural levels of the complexes have been calculated. The
centrality measures reveal valuable structural information including
information about those vertices that are more likely to participate in
higher-order interactions, as well as inform whether there is a difference in
the ranks of vertices for these higher-order networks based on graph centrality
and simplicial centrality measures.
