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Higher-order social-ecological network as a simplicial complex

A social-ecological network is a formal representation of a corresponding social-ecological system, and encodes a relation within a given system as an interaction. Conventionally, such networks have been defined as encoding and representing pairwise interactions among the fundamental units of the system. This work proposes a combinatorial definition of social-ecological network by means of its structure as a simplicial complex. The proposed definition is a comprehensive one that takes into account the heterogeneity of interactions within a given SES, and the higher-order social-ecological network modelled using this definition is able to represent the modelled SES by capturing all orders of interactions within the system. Such a social-ecological network consequently, is better equipped to capture and represent the structural details of the real-world SES, and is thus capable of facilitating a deeper insight into the complex behaviour of the represented SES emergent through the higher-order interactions within the system, as compared to the conventional graph-theoretic network that exclusively models pairwise interactions.