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
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-τ)/2) | α = 2 |
Tangent-based | tanhomoτ,α(V1, V2, W) | W- α (1-W) tan(π (D-τ)/2) | α = 2 |
Exponential | exphomoτ,σ(V1, V2, W) | 1 - (1-W) eσ(D-τ) | σ = 10 |