A single-valued neutrosophic extension of adaptive-agent-based network models for the study of host–guest interactions in migration contexts is proposed. Unlike the classical formulation developed by Chuang, Chou, and D’Orsogna, each agent is described by a single-valued neutrosophic attitude ⟨T, I, F⟩ ∈ [0, 1]3, quantifying, respectively, the propensity toward integration-oriented acceptance (T), indeterminacy (I), and segregation-oriented rejection (F). Compared with a purely scalar attitude model, this framework separates acceptance, refusal, and undecidedness, which is crucial in migration contexts where an observed moderate position may correspond either to a genuine compromise or to unresolved ambiguity. Moreover, it captures key characteristics of social interactions more effectively. The proposed model contributes in three main directions. First, the network structure is extended from the Erdős-Rényi random baseline to Watts-Strogatz small-world and Barabási–Albert-type scale-free topologies. Second, the utility function is made capacity-dependent: agents with higher socioeconomic reward and higher neutrosophic scores can maintain more social connections without a proportional loss of effectiveness. Third, the rewiring process is refined by combining multi-agent Q-learning with a Dezert-Smarandache-inspired trust aggregation mechanism. This allows agents to learn whether keeping, adding, or deleting social ties is advantageous over the long term, while candidate selection combines pairwise similarity with trust, prestige, and degree-based visibility. Numerical simulations compare random, small-world, and scale-free networks, examine the evolution of an integration index, and illustrate how the model can be used to scan migrant-fraction sensitivity and possible neighbourhood-tipping thresholds.