Assessing Graph Robustness through Modified Zagreb Index

Graph robustness or network is the ability that a graph preserves its connectivity other properties after loss of vertices and edges, which has been central problem in research complex networks. In this paper, we introduce Modified Zagreb index centrality as novel measures to study robustness. We theoretically find some relationships between these measures. Then, use analyze BA scale-free networks, ER random graphs WS small world networks under deliberate vertex attacks. also correlations new measure existed Finally, two real All results demonstrate efficiency for assessing