Fig 1.
Opinion formation on the star graph.
Fig 2.
x1(t + 1) as a function of x2,3,4,5(t).
(a) β1 = 1, b1 = 1, x1(t) = 0; (b) β1 = 2.5, b1 = 1, x1(t) = 0.25.
Fig 3.
Graphical illustration of Case 2 from Theorem 1 (i.e. p < 0 and β ≥ −1/p).
(a) For values of y(t) in the green range, y(t) will converge to y = p. (b) For values of y(t) in the red range, y(t) will diverge to y = 1. (c) For , y(t) will not change such that
.
Fig 4.
(a) the distribution of βP for 10,000 random opinion vectors (uniform on [−1, 1]); For one of the opinion vectors, (b) the variance of all converged y as β increases from 0 to 10; (c) consensus opinion values for β ∈ [0, 2.1]; (d) final converged opinions for each of the nodes.
Fig 5.
For 1,000 random y(0) on Karate network.
(a) consensus opinion when β = 1; (b) mean polarized opinion when β = 10.
Fig 6.
Based on one ER model (n = 100, ρ = 0.0606), one WS model (n = 100, K = 6, σ = 0.2), and one BA model (n = 100, M0 = 4, M = 3).
(a) distribution of βP for 1,000 random opinion vectors; (b) for 1,000 opinion vectors, the relation between the consensus value and the mean y(0) when β = 1.
Fig 7.
Based on three WS models with different rewiring probabilities (n = 100, K = 6, σ = 0.1, 0.3, 0.8).
(a) distribution of βP for 1,000 random opinion vectors; (b) for 1,000 opinion vectors, the relation between the consensus value and the mean y(0) when β = 1.
Table 1.
βP for real-world twitter datasets.