Filter can characterize Moore-Smith convergence theory in general topology. It is different from net

and its properties are more initial. But there is no figure for filters graph on arbitrary set. In this paper

filter

on finite set

is characterized. There is only principle filter on finite set

and it can be determined by its generating set. Then filters graph is defined as graph game. The Sprague-Grundy function of filters graph is analyzed

and each position in filters graph is studied. The condition

which the position is P-position

is show. Finally

sum and product of filters graphs are researched. And by the Sprague-Grundy function

filters graphs

even sum and product

are drawn in some cases.