Hierarchical Reconstruction of the Cosmic Web, The H-Spine method

The cosmic web consists of a nested hierarchy of structures: voids, walls, filaments, and clusters. These structures interconnect and can encompass one another, collectively shaping an intricate network. Here we introduce the Hierarchical Spine (H-Spine) method, a framework designed to hierarchically identify and characterize voids, walls, and filaments. Inspired by the geometrical and dynamical constraints imposed by anisotropic gravitational collapse, the H-Spine method captures the geometry and interconnectivity between cosmic structures as well as their nesting relations, offering a more complete description of the cosmic web compared to single-scale or multi-scale approaches. To illustrate the method's utility, we present the distribution of densities and sizes of voids, walls and filaments identified in a 3-level hierarchical space. This analysis demonstrates how each level within the hierarchy unveils distinctive densities and scales inherent to cosmic web elements.