  Reduction of frustration was the driving force in an approach to social
balance as it was recently considered by Antal \emph{et al.} [ T. Antal, P. L.
Krapivsky, and S. Redner, Phys. Rev. E {\bf 72}, 036121 (2005). ]. We
generalize their triad dynamics to $k$-cycle dynamics for arbitrary integer
$k$. We derive the phase structure, determine the stationary solutions and
calculate the time it takes to reach a frozen state. The main difference in the
phase structure as a function of $k$ is related to $k$ being even or odd. As a
second generalization we dilute the all-to-all coupling as considered by Antal
\emph{et al.} to a random network with connection probability $w<1$. ...
