Fig 1.
(a) An example of a bipartite graph, which is composed of two disjoint sets of nodes m and f. There is no link between nodes in the same set and the connection between sets is characterized by degree distribution P(k). (b) The action scheme of the mate choosing process. Two nodes i and j have to undergo an intermediate stage to reach the stable long term relation. During the intermediate stage nodes i and j are also available to build relationship with other nodes. If this happens they break and their relationship is back to the initial state.
Fig 2.
(a) The Pearson coefficient of correlation ρ of the attractiveness between the two coupled individuals in different systems. ρ is strongest in fully-connected systems. In sparse networks, ρ increases monotonically with the average degree ⟨k⟩ and decreases with the degree diversity. For all cases investigated, system size is 2N and N = 10,000. (b) The average attractiveness of individuals in the set f who are matched with those in a subset of m with attractiveness in the range [am−0.05, am+0.05) for a series of points am. 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. (c) The attractiveness contour figure of the coupled individuals in Erdős-Rényi networks with average degree ⟨k⟩ = 5. A pattern emerges even when similarity is not the motivation in seeking partners. am and af are the attractiveness of nodes in sets m and f, respectively. (d) The attractiveness contour figure of the coupled individuals in fully-connected systems. The correlation is strongest towards the less attractive individuals (the circled part).
Fig 3.
(a, b) The probability of failing to be matched conditioned on attractiveness a and degree k (Pnot(a, k)) decreases exponentially with a and k in scale-free networks with P(k) ∼ k−γ, γ = 3 and ⟨k⟩ = 5.
Fig 4.
The Pearson coefficient of correlation ρ of the attractiveness between the two coupled individuals in Erdős-Rényi networks with size 2N (N = 10,000) and varying average degree ⟨k⟩.
ρ increases monotonically in all three cases analyzed. However, ρ is largest in networks where the degree and the attractiveness are positively correlated. When they are negatively correlated, ρ is weakest and can even be negative.
Fig 5.
(a) The size of the maximum matching nmax increases monotonically with the average degree ⟨k⟩ in different networks. (b) The number of matched couples n increases monotonically with the average degree ⟨k⟩ in different networks. (c) The ratio between the number of matched couples and the size of the maximum matching (R = n/nmax) varies non-monotonically with the average degree ⟨k⟩. (d) Different behaviors of R in Erdős-Rényi networks where the correlation between degree and the attractiveness varies. Negative correlation between the degree and the attractiveness yields the largest R while positive correlation between the degree and the attractiveness results in the smallest R. Networks tested in all cases are with size 2N (N = 10,000).