  Algorithms for search of communities in networks usually consist discrete
variations of links. Here we discuss a flow method, driven by a set of
differential equations. Two examples are demonstrated in detail. First is a
partition of a signed graph into two parts, where the proposed equations are
interpreted in terms of removal of a cognitive dissonance by agents placed in
the network nodes. There, the signs and values of links refer to positive or
negative interpersonal relationships of different strength. Second is an
application of a method akin to the previous one, dedicated to communities
identification, to the Sierpinski triangle of finite size. During the time
evolution, the related graphs are weighted; yet at the end the discrete
character of links is restored. In the case of the Sierpinski triangle, the
method is supplemented by adding a small noise to the initial connectivity
matrix. By breaking the symmetry of the network, this allows to a successful
handling of overlapping nodes.
