#maximal-cliques

Question 1: Single choice

Which family of Gibbs distributions is induced by the undirected graph below (all distributions that factorise over it)?

$p \propto \phi_1(x_1,x_2,x_3,x_4)\,\phi_2(x_3,x_4,x_5,x_6)$ 1
$p \propto \phi_1(x_1,x_2,x_4)\,\phi_2(x_1,x_3,x_4)\,\phi_3(x_3,x_4,x_5,x_6)$ 2
A product of nine pairwise factors, one per edge3
$p \propto \phi_1(x_1,x_2,x_4)\,\phi_2(x_1,x_3,x_4)\,\phi_3(x_3,x_4,x_5)\,\phi_4(x_4,x_5,x_6)$ 4