Generalized network structures: The configuration model and the canonical ensemble of simplicial complexes

Understand

Simplicial complexes are generalized network structures able to encode interactions occurring between more than two nodes.

• Simplicial complexes describe a large variety of complex interacting systems ranging from brain networks, to social and collaboration networks.
• Here we characterize the structure of simplicial complexes using their generalized degrees that capture fundamental properties of one, two, three or more linked nodes.
• Moreover we introduce the configuration model and the canonical ensemble of simplicial complexes, enforcing respectively the sequence of generalized degrees of the nodes and the sequence of the expected generalized degrees of the nodes.