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We define a Tanaka's equation on an oriented graph with two edges and twovertices. This graph will be embedded in the unit circle. Extending thisequation to flows of kernels, we show that the laws of the flows of kernels $K$solution of Tanaka's equation can be classified by pairs of probabilitymeasures $(m^+,m^-)$ on $[0,1]$, with mean 1/2. What happens at the firstvertex is governed by $m^+$, and at the second by $m^-$. For each vertex $P$,we construct a sequence of stopping times along which the image of the wholecircle by $K$ is reduced to $P$. We also prove that the supports of these flowscontains a finite number of points, and that except for some particular casesthis number of points can be arbitrarily large.

Tanaka's equation on the circle and stochastic flows