Instability in the Centers of Radially Induced Subgraphs

Centrality measures identify vertices that are potentially important when compared to the rest of the graph. When applied to an induced subgraph for which all vertices are within a given radius of the center, we sometimes find the center of the subgraph is different. Here, we provide some insight into how these “fulcrum” points can arise in graphs, and show that the degree to which the center can change is generally unbounded.