  Dynamically changing graphs are used in many applications of graph
algorithms. The scope of these graphs are in graphics, communication networks
and in VLSI designs where graphs are subjected to change, such as addition and
deletion of edges and vertices. There is a rich body of the algorithms and data
structures used for dynamic graphs. The paper overview the techniques and data
structures used in various dynamic algorithms. The effort is tried to find out
the comparison in these techniques namely the hierarchical decomposition of
graphs and highlighting the ingenuity used in designing these algorithms.
