Table 2.

The behaviour of the duplication–divergence network of arbitrary symmetry for different values of probabilities to preserve a link σ₁ and σ₂. Here, L(N) is the average number of links for a given number of nodes N, n_k the average fraction of nodes of degree k. $σ_{i}^{*}$ , i = 1, 2 are the solutions of equation (5), γ(σ₁, σ₂) is given by equation (9).

σ	Self-averaging	L(N)	n_k
σ₁ = σ₂ = 1	No	N(N + 1)/6	2(N − k)/[N(N − 1)]
3/2 < σ₁ + σ₂ < 1	No	~N^{2(σ₁+σ₂−1)}	~N^{3−2σ₁−2σ₂}F(k/N^{2σ₁+2σ₂−3)}
σ₁ + σ₂ < 3/2, σ_i > $σ_{i}^{*}$ , i = 1, 2	Yes	~N ln N	probably ~k⁻²
1/2 < σ₁ + σ₂, σ_i < $σ_{i}^{*}$ , i = 1, 2	Yes	~N	~k^{−γ(σ₁,σ₂)}