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The significance of a vertex is determined by its local and global environments in a network and can be better represented by a set of topological parameters. In cases A, B and C, the degree of vertex 2 is the same. However, its betweenness centrality in A, B and C is high, low and high, respectively, and the parwise disconnectivity index in A, B and C is high, low and low, respectively. Thus, focusing on betweenness centrality may yield to misleading conclusions.
