Abstract

We consider two simple asynchronous opinion dynamics on arbitrary graphs where every node u of the graph has an initial value xi(u)(0). In the first process, which we call the Nodemodel, at each time step t >= 0, a random node.. and a random sample of k of its neighbours v(1), v(2), . . . , v(k) are selected. Then, u updates its current value xi(u)(t) to xi(u)(t + 1) = alpha xi(u) (t) + (1-alpha)/k Sigma(k)(i-1) xi(vi)(t), where alpha is an element of(0, 1) and k >= 1 are parameters of the process. In the second process, called the. Edgemodel, at each step a random pair of adjacent nodes (u , v) is selected, and then nodeu updates its value equivalently to the Nodemodel with k = 1 and v as the selected neighbour.