Skip to main content

Table 2 Different options for combination functions \( {\mathbf{c}}_{\upomega_{X,Y}}\left({V}_1,{V}_2,W\right) \) for the homophily principle based on a tipping point τ; for the graphs depending on D =  V1 – V2, see Fig. 3

From: Mathematical analysis of the emergence of communities based on coevolution of social contagion and bonding by homophily

Function type Function name Numerical representation Parameters in Fig. 3
Simple Linear slhomoτ, α(V1, V2, W) W + α W (1-W) (τ- D) α = 6
Simple quadratic 1 sq1homoτ, α(V1, V2, W) W + α W (1- W) (τ2 – D2) α = 6
Simple quadratic 2 sq2homoτ, α, δ(V1, V2, W) W + α ((τ + δ)2 - (D + δ)2) δ = 0.15, α = 10
Cubic cubehomoτ, α(V1, V2, W) W + α (1-W) (1-D/τ)3 α = 0.9
Logistic 1 log1homoτ,σ(V1, V2, W) \( \frac{W}{W+\left(1-W\right)\ {\mathrm{e}}^{\upsigma \left(D-\uptau \right)}} \) σ = 10
Logistic 2 slog2homoτ,σ,α(V1, V2, W) \( W+\upalpha\ \frac{W\left(1-W\right)\ }{1+{\mathrm{e}}^{-\upsigma \left(D-\uptau \right)}} \) σ = 4, α = 5
Sine-based sinhomoτ,α(V1, V2, W) W - α (1-W) sin(π (D)/2) α = 2
Tangent-based tanhomoτ,α(V1, V2, W) W- α (1-W) tan(π (D)/2) α = 2
Exponential exphomoτ,σ(V1, V2, W) 1 - (1-W) eσ(D) σ = 10