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This work is intended on identification with basic problems from the graphs theory area. There are the basic conceptions as well more complicated problems described. The one part of this work is specialized in working of individual types of graphs. It starts with single linked list through double linked list after as much as trees which represented the simplest graphs textures. The other part of this work devotes to the whole graph and describes more complicated problems and their resolution from the theory graphs area. Among these problems belongs to searching in graphs help by Depth First Search and Breadth First Search methods. Then searching the shortest way help by the specific algorithms as are: Dijkstra´s algorithm, Floyd-Warshall´s algorithm and Bellman-Ford´s algorithm. The last part is devoted to problems with searching minimal frames of graphs with usage Kruskal´s algorithm, Jarnik´s algorithm and Boruvka´s algorithm methods.