In ΛCDM, the way galaxies, halos, and clusters are connected by filaments—quantified by graph-based or topological connectivity statistics such as node degree, number of filaments per halo, and junction multiplicity—should follow from the Gaussian initial density field and standard hierarchical growth, and simulations predict a relatively well-defined distribution of connections per node once mass and environment are fixed (Bond et al. 1996; Cautun et al. 2014). Observations and high-resolution simulations, however, often show either too many multi-filament junctions, overly connected massive nodes, or different connectivity–mass and connectivity–environment relations than basic ΛCDM plus halo-model expectations, hinting at missing dynamics, non-Gaussian initial conditions, or limitations in how the standard model builds the cosmic web’s graph structure (Codis et al. 2018; Darragh-Ford et al. 2019).