For distinct vertices u and v in a graph G, the connectivity between u and v, denoted \(\kappa _G(u,v)\), is the maximum number of internally disjoint u–v paths in G. The average connectivity of G, denoted \({\overline{\kappa }}(G),\) is the average of \(\kappa _G(u,v)\) taken over all unordered pairs of distinct vertices u, v of G. Analogously, for a directed graph D, the connectivity from u to v, denoted \(\kappa _D(u,v)\), is the maximum number of internally disjoint directed u–v paths in D. The average connectivity of D, denoted \({\overline{\kappa }}(D)\), is the average of \(\kappa _D(u,v)\) taken over all ordered pairs of distinct vertices u, v of D. An orientation of a graph G is a directed graph obtained by assigning a direction to every edge of G. For a graph G, let \({\overline{\kappa }}_{\max }(G)\) denote the maximum average connectivity among all orientations of G. In this paper we obtain bounds for \({\overline{\kappa }}_{\max }(G)\) and for the ratio \({\overline{\kappa }}_{\max }(G)/{\overline{\kappa }}(G)\) for all graphs G of a given order and in a given class of graphs. Whenever possible, we demonstrate sharpness of these bounds. This problem had previously been studied for trees. We focus on the classes of cubic 3-connected graphs, minimally 2-connected graphs, 2-trees, and maximal outerplanar graphs.

对于不同的顶点ù和v中的曲线图G ^，所述连接之间ù和v，表示为\（\卡帕_G（U，V）\） ，是最大的内部不相交数ü - v在路径G ^。G的平均连通性，表示为\({\overline{\kappa }}(G),\)是\(\kappa _G(u,v)\)对不同顶点u ,  v 的所有无序对的平均值的G。类似地，对于有向图D，从u到v 的连通性，表示为\(\kappa _D(u,v)\)，是D中内部不相交的有向u – v路径的最大数量。D的平均连通性，表示为\({\overline{\kappa }}(D)\)，是\(\kappa _D(u,v)\)对不同顶点u ,  v 的所有有序对所取的平均值的d。图G的方向是通过为G 的每条边指定方向而获得的有向图。对于图G, 让\({\overline{\kappa }}_{\max }(G)\)表示G 的所有方向之间的最大平均连通性。在本文中，我们获得了\({\overline{\kappa }}_{\max }(G)\)和比率\({\overline{\kappa }}_{\max }(G)/ {\overline{\kappa }}(G)\)用于给定顺序和给定图类中的所有图G。只要有可能，我们就会展示这些边界的锐度。这个问题以前曾针对树木进行过研究。我们专注于三次 3 连通图、最小 2 连通图、2 树和最大外平面图的类。