The eccentric connectivity index of a graph G is \(\xi ^c(G) = \sum _{v \in V(G)}\varepsilon (v)\deg (v)\), and the eccentric distance sum is \(\xi ^d(G) = \sum _{v \in V(G)}\varepsilon (v)D(v)\), where \(\varepsilon (v)\) is the eccentricity of v, and D(v) the sum of distances between v and the other vertices. A lower and an upper bound on \(\xi ^d(G) - \xi ^c(G)\) is given for an arbitrary graph G. Regular graphs with diameter at most 2 and joins of cocktail-party graphs with complete graphs form the graphs that attain the two equalities, respectively. Sharp lower and upper bounds on \(\xi ^d(T) - \xi ^c(T)\) are given for arbitrary trees. Sharp lower and upper bounds on \(\xi ^d(G)+\xi ^c(G)\) for arbitrary graphs G are also given, and a sharp lower bound on \(\xi ^d(G)\) for graphs G with a given radius is proved.

图G的偏心连接指数为\（\ xi ^ c（G）= \ sum _ {v \ in V（G）} \ varepsilon（v）\ deg（v）\），并且偏心距离和为\（\ xi ^ d（G）= \ sum _ {v \ in V（G）} \ varepsilon（v）D（v）\），其中\（\ varepsilon（v）\）是v的离心率，和D（v）v与其他顶点之间的距离之和。为任意图G给出\（\ xi ^ d（G）-\ xi ^ c（G）\）的上下限。直径最大为2的正则图和带有完整图的鸡尾酒会图的连接分别形成获得两个相等性的图。为任意树给出\（\ xi ^ d（T）-\ xi ^ c（T）\）的尖锐上下限。夏普降低和上界\（\ XI ^ d（G）+ \ XI ^ C（G）\）对任意图形ģ也给出，和一个尖锐的下部上结合\（\ XI ^ d（G）\）证明了具有给定半径的 图G。