Current & Upcoming

Higher-order networks have become a popular tool in the network science community to model dynamics such as synchronization and diffusion. The linearized system often depends on a Laplacian operator and its spectral properties. We introduce a Laplacian operator for uniform hypergraphs and study the limiting operator for an increasing sequence of dense uniform hypergraphs using the theory of graph limits. Although a theory of dense hypergraph limits has been developed by Elek and Szegedy, and independently Zhao, not much of its implications to spectral properties is known. We show that a weaker notion of convergence for the sequence of hypergraphs is sufficient to obtain pointwise convergence of the spectrum of the Laplacians.