We consider a class of inhomogeneous random graphs G_n(α, ε) where n vertices carry i.i.d. Pareto weights (Wi)i∈[n] with tail index α > 0. Conditionally on the weights, edges are drawn independently with probability pij = min(εWiWj , 1), where ε = ε_n controls sparsity. The behavior of the model is driven by the tail index α, with a sharp structural change at the boundary α = 1. The infinite-mean and finite-mean regimes lead to fundamentally different emerging landscapes. Building on recent work of L. Avena, D. Garlaschelli, R.S. Hazra and M. Lalli (Journal of Applied Probability 2025), we analyze the degree asymptotics across the full range α > 0 and identify the relevant scalings of ε_n in each regime for the convergence in distribution of the typical degree. We then characterize the connectivity threshold. In the infinite-mean case α ≤ 1, connectivity is hub-driven and forces a collapse of the diameter to at most two. In the finite-mean regime α > 1, connectivity emerges through a collective mechanism at a density scale distinct from that of ultra-small-world behaviour. This is joint ongoing work with Luisa Andreis, Luca Avena and Rajat Hazra.