Spectral clustering (SC) is a popular approach for gaining insights from complex networks. Conventional SC focuses on second-order structures (e.g. edges) without direct consideration of higher-order triangles). This has motivated extensions that directly consider structures. However, both approaches are limited to considering single order. To address this issue, paper proposes novel Mixed-Orde...

In this paper we present a unified framework for constructing spectrally equivalent low-order-refined discretizations the high-order finite element de Rham complex. This theory covers diffusion problems in $H^1$, $H({\rm curl})$, and div})$, is based on combining low-order discretization posed refined mesh with basis N\'ed\'elec Raviart-Thomas elements that makes use of concept polynomial histo...