graphs, which accounts only for a small fraction of all graphs. This fact suggests that GI may not be very hard. In fact, GI is well solved from practical point of view and there are a number of efficient algorithms available [@McP]. Even from worst-case point of view, GI may not be as hard as NP-complete problems. As a matter of fact GI is not NP-complete unless the polynomial hierarchy collapses to its second level [@BHZ; @Schonig]. On the other hand, however, we have no efficient algorithm so far for general graphs in worst-case analysis, while for restricted graph classes there are efficient algorithms, for instance, for graphs with bounded degree [@Luks] and for graphs with bounded eigenvalue multiplicity [@BaGrMu]. L. Babai [@Babai] recently declared an algorithm resolving GI for any graph of order $n$ within time $\exp\big\{ (\log n)^{O(1)} \big\}$ in worst-case analysis. In the present paper, we develop a machinery for GI from geometric point of view, which enables us devise a deterministic algorithm solving GI for any graph of order $n$ within time $2^{ O\left( \log^2 n \right) }$ in worst-case analysis.

In the case that two graphs $G$ and $H$ involved are the same, an isomorphism 