Abstract
This paper analyzes the robustness of the network based on the centrality of vertices in the graph. In this paper, a random graph is generated and a modified graph is constructed by adding or removing vertices or edges in the generated random graph. And then we analyze the robustness of the graph by observing changes in the centrality of the random graph and the modified graph. In the process modifying a graph, we changes some parts of the graph, which has high values of centralities, not in the whole. We study how these additional changes affect the robustness of the graph when changes occurring a group that has higher centralities than in the whole.