Taking account for the graph randomness, our purpose is a node classification by their extremal indexes
(EI) as the local dependence measure of node influence characteristics. The EI was calculated by node
PageRanks of the local tree related to the node, which is a kind of Thorny Branching Tree (TBT). The
blocks estimator was used for the EI estimation by sliding and disjoint block definitions. The classification
by the node EI value and the average block size for the local node TBT was introduced for simulated
graphs by the Forest Fire and Erdős-Rényi Models and the Berkeley-Stanford dataset as a real example.
The new classification methodology is proposed irrespective on the graph structure.
