An Analysis of the Matching Hypothesis in Networks

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

An Analysis of the Matching Hypothesis in Networks - Fig 2

<p><b>(a)</b> The Pearson coefficient of correlation <i>ρ</i> of the attractiveness between the two coupled individuals in different systems. <i>ρ</i> is strongest in fully-connected systems. In sparse networks, <i>ρ</i> increases monotonically with the average degree ⟨<i>k</i>⟩ and decreases with the degree diversity. For all cases investigated, system size is 2<i>N</i> and <i>N</i> = 10,000. <b>(b)</b> The average attractiveness </p><p></p><p></p><p></p><p></p><p><mi>a</mi><mo>¯</mo></p><mi>f</mi><p></p><p></p><p></p><p></p> of individuals in the set <i>f</i> who are matched with those in a subset of <i>m</i> with attractiveness in the range [<i>a</i>_<i>m</i>−0.05, <i>a</i>_<i>m</i>+0.05) for a series of points <i>a</i>_<i>m</i>. In fully-connect systems, the less attractive individuals are bound to be coupled with ones who are also less attractive. In sparse networks, however, they are coupled with ones who are more attractive. <b>(c)</b> The attractiveness contour figure of the coupled individuals in Erdős-Rényi networks with average degree ⟨<i>k</i>⟩ = 5. A pattern emerges even when similarity is not the motivation in seeking partners. <i>a</i>_<i>m</i> and <i>a</i>_<i>f</i> are the attractiveness of nodes in sets <i>m</i> and <i>f</i>, respectively. <b>(d)</b> The attractiveness contour figure of the coupled individuals in fully-connected systems. The correlation is strongest towards the less attractive individuals (the circled part).<p></p