In this paper we investigate the structural properties of betweenness centrality and determine some cases in which betweenness reaches its extremal values. Special attention is paid to Star(G), the set of vertices adjacent to all other vertices in a graph and we prove several results about the betweenness of the elements of this set. We introduce the new concept of total betweenness and relate it to group betweenness. We prove a necessary and sufficient condition for the two measures to coincide. Next we consider cutsets and cutvertices and we find a lower bound for their betweenness; in particular for a cutvertex this lower bound is the cutting number. Finally we apply the previous results to trees, proving an alternative formula for betweenness based oil cutvertex properties.
|Titolo della pubblicazione ospite||TOPOLOGY AND DYNAMICS: THEORY AND APPLICATIONS TO ECONOMIC AND SOCIAL SYSTEMS, Lectures Notes in Economics and Mathematical Systems|
|Editor||STEFANI Silvana, TORRIERO Anna NAIMZADA Ahmad|
|Numero di pagine||15|
|Stato di pubblicazione||Pubblicato - 2009|
|Nome||LECTURE NOTES IN ECONOMICS AND MATHEMATICAL SYSTEMS|