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 i
nto 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.
A set of $N$ points is chosen randomly in a $D$-dimensional volume $V=a^D$, with periodic boundary conditions. For each point $i$, its distance $d_i$ is found to its nearest neighbour. Then, the maximal value is found, $d_{max}=max(d_i, i=1,...,N)$.
Our numerical calculations indicate, that when the density $N/V$=const, $d_{max}$ scales with the linear system size as $d^2_{max}propto a^phi$, with $phi=0.24pm0.04$ for $D=1,2,3,4$.
