Cross-linking a single polymer chain with itself leads to soft nanoparticles with well-defined properties. We study such single-chain nanoparticles (SCNP) obtained by cross-linking in good and in poor solvents using Monte Carlo simulations and theoretical models. We show that SCNP obtained by cross-linking in poor solvents preserve their shape during swelling in good solvents only if the precursor chain is very long. In this case the Flory Rehner model describes the swelling of SCNP. Shorter chains and SCNPs cross-linked in good solvent generate noncompact structures. Here we obtain a good theoretical description of the simulated swelling properties using a mean-field model by taking into account the cross-linking topology using the connectivity matrix of the cross-linked chain. The crossover between the two regimes can consistently be described using a scaling argument. We further show that the distances between cross-links along the chain contour follows the distribution for Gaussian chains after cross-linking under poor solvent conditions.