Gibbs Distribution (with pairwise interactions) Gibbs distribution u:o∈[g]' network G,E): L(a)Ae(ou;ou)bo() e=(u,v)∈E v∈V independent set: bv a-B司6-图 coloring: 10 1 1 Ae= bu= .H Ae:[q]×[q]→[0,1] 1 bm:[q]→[0,1]Gibbs Distribution • Gibbs distribution µ : ∀σ∈[q]V µ(￾) / Y e=(u,v)2E Ae(￾u, ￾v) Y v2V bv(￾v) • independent set: bv =  1 1 ￾ Ae =  1 1 1 0￾ • coloring: network G(V,E): Ae u bv v Ae: [q] × [q] → [0,1] bv: [q] → [0,1] (with pairwise interactions) Ae = 2 6 6 6 4 0 0 ... 0 3 7 7 7 5 1 1 bv = 2 6 4 1 . . . 1 3 7 5