  The matching hypothesis in social psychology claims that people are more
likely to form a committed relationship with someone equally attractive.
Previous works on stochastic models of human mate choice process indicate that
patterns supporting the matching hypothesis could occur even when similarity is
not the primary consideration in seeking partners. Yet, most if not all of
these works concentrate on fully-connected systems. Here we extend the analysis
to networks. Our results indicate that the correlation of the couple's
attractiveness grows monotonically with the increased average degree and
decreased degree diversity of the network. This correlation is lower in sparse
networks than in fully-connected systems, because in the former less attractive
individuals who find partners are likely to be coupled with ones who are more
attractive than them. The chance of failing to be matched decreases
exponentially with both the attractiveness and the degree. The matching
hypothesis may not hold when the degree-attractiveness correlation is present,
which can give rise to negative attractiveness correlation. Finally, we find
that the ratio between the number of matched couples and the size of the
maximum matching varies non-monotonically with the average degree of the
network. Our results reveal the role of network topology in the process of
human mate choice and bring insights into future investigations of different
matching processes in networks.
