Simplicial structures in ecological networks

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.