  We consider infinite graphs and the associated energy forms. We show that a
graph is canonically compactifiable (i.e. all functions of finite energy are
bounded) if and only if the underlying set is totally bounded with respect to
any finite measure intrinsic metric. Furthermore, we show that a graph is
canonically compactifiable if and only if the space of functions of finite
energy is an algebra. These results answer questions in a recent work of
Georgakopoulos, Haeseler, Keller, Lenz, Wojciechowski.
