  Arakelov-Green functions defined on metrized graphs have important role in
relating arithmetical problems on algebraic curves into graph theoretical
problems. In this paper, we clarify the combinatorial interpretation of certain
Arakelov-Green functions by using electric circuit theory. The formulas we gave
clearly show that such functions are piece-wisely defined, and each piece is a
linear or quadratic function on each pair of edges of metrized graphs. These
formulas lead to an algorithm for explicit computation of Arakelov-Green
functions.
