Betweenness centrality is a measure of the importance of a vertex x inside a network based on the fraction of shortest paths passing through x. We study a blow-up construction that has been shown to produce graphs with uniform distribution of betweenness. We disprove the conjecture about this procedure's universality by showing that trees with a diameter at least three cannot be transformed into betweenness-uniform by the blow-up construction. It remains open to characterize graphs for which the blow-up construction can produce betweenness-uniform graphs.
翻译:中间中心点是衡量一个网中顶点 x 的重要性的一种尺度,这个网中以通过x的最短路径的分数为基础。 我们研究了一个爆炸性构造,已经显示它能产生具有统一分布的图表。 我们通过显示直径至少为三的树木无法通过爆炸构造而转化成不一致性之间的图解,来否定关于这一程序普遍性的推测。 我们仍然可以对爆炸性构造能够产生不统一图形的图形进行定性。