Hi everyone! Could you help me with this question please?

Prove that if G is a finite connected graph, then every harmonic function on G is constant.

If G is infinite, must every harmonic function be constant?

Note: A function f:V(G)-> R is harmonic if, for every u in V(G)

f(u)= (1/d(u))* S f(w) (w in N(u))

Thank you in advance!!