Peripherality in networks: theory and applications

We investigate several related measures of peripherality and centrality for vertices edges in networks, including the Mostar index which was recently introduced as a measure both networks. refute conjecture on maximum possible bipartite graphs. asymptotically answer another problem difference between irregularity trees. also prove number extremal bounds computational complexity results about index, irregularity, centrality. discuss graphs where is not an accurate peripherality. construct general family with property that strictly greater are closer to center. two represent SuperFast MOZART-4 systems atmospheric chemical reactions by computing various these For graphs, we find than edges. introduce some new indices perform well