Betweenness centrality is a centrality measure based on the overall amount of shortest paths passing through a given vertex. A graph is betweenness-uniform if all its vertices have the same betweenness centrality. We study the properties of betweenness-uniform graphs. In particular, we show that every connected betweenness-uniform graph is either a cycle or a $3$-connected graph. Also, we show that betweenness uniform graphs of high maximal degree have small diameter.
翻译:中间点是一个基于通过给定顶点的短路总长度的中央度测量标准。 如果所有顶端具有相同的中间点, 图形就是中间线- 统一线。 我们研究内分- 统一线图的特性。 特别是, 我们显示每个连接的内分点- 统一线图要么是一个周期, 要么是一个三美元的连接图。 另外, 我们显示, 高度的中间线统一图的直径较小 。