Stable matching studies how to pair members of two sets with the objective to achieve a matching that satisfies all participating agents based on their preferences. In this research, we consider the case of matching in a social network where agents are not fully connected. We propose the concept of D-neighbourhood associated with connective costs to investigate the matching quality in four types of well-used networks. A matching algorithm is proposed based on the classical Gale-Shapley algorithm under constraints of network topology. Through experimental studies, we find that the matching outcomes in scale-free networks yield the best average utility with least connective costs comparing to other structured networks. This research provides insights for understanding matching behavior in social networks like marriage, trade, partnership, online social and job search.
Ling, Y., Wan, T., & Qin, Z. (2016). Stable matching in structured networks. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9806 LNCS, pp. 271–280). Springer Verlag. https://doi.org/10.1007/978-3-319-42706-5_21