This scheme is based on the newly introduced notion of volatility of separate clusters as well as of whole classification. <...> It describes the stability, exactness, validity of subsets of the given initial set – in essence, their possibility (or impossibility) to be selected as clusters. <...> The suggested algorithm finds the clusters with arbitrary levels of volatility, including the conventional case of zero volatility. <...> The clusters in USA, Russia and Sweden stock market (for crisis period of 2008-2010) and deputies clusters based on voting results in the 3rd State Duma between September 2001 and January 2002 (the period including the creation of the party ”United Russia” 01.12.2001) were constructed by the suggested algorithm. <...> But several indices (i.e. concordance of parties’ positions) did not show sensible jumps near this political ”bifurcation point”. <...> The other considered various model examples demonstrated the results well-coordinated with geometrical intuition. <...> Key words and phrases: cluster analysis, automatic classification, volatility, cut in graph, stock market, State Duma. 1. <...> Introduction The well-known clustering problem consists in selection from a given set of objects which takes into account the volatility of subsets of the given initial set. <...> Volatility is determined formally for separate candidates as well as for the whole clustering problem. <...> Let us consider some examples without giving exact definition of volatility but several non-intersecting subsets (usually called clusters, aggregates, blocks, classes, etc.). <...> It is required that every cluster consists of objects that are in some sense closely connected, similar in appearance, while objects belonging to different clusters are as unlike as possible, significantly distinct. <...> In classification problems it is required additionally that the selected clusters form a division of the initial set, but the abandoning of this requirement seems more realistic in the considered situations. <...> Intuitively cluster 1 has the same volatility 0, cluster 2 has some small volatility, and volatility of cluster 3 exceeds volatility of cluster 2. <...> Finally the cluster 3 in Fig. 1d practically disappears (its volatility is close to the maximal number 1), meanwhile clusters 1 in all the pictures has the same volatility, as well as cluster 2 in Fig. 1c and 1d. <...> Clusters with different volatility <...>