In this paper, we prove two existence results of solutions to mean field equations
Δu+e^u=ρδ_0
and
Δu=λe^u(e^u−1)+4π\sum_{j=1}^M δ_{p_j}
on an arbitrary connected finite graph, where ρ>0 and λ>0 are constants, M is a positive integer, and p_1,…,p_M are arbitrarily chosen distinct vertices on the graph.