In this paper, we study the eccentric distance sum of substitution tree networks. Calculation of eccentric distance sum naturally involves calculation of average geodesic distance and it is much more complicated. We obtain the asymptotic formulas of average geodesic distance and eccentric distance sum of both symmetric and asymmetric substitution tree networks. Our result on average geodesic distance generalizes the result of [T. Li, K. Jiang and L. Xi, Average distance of self-similar fractal trees, Fractals 26(1) (2018) 1850016.] from symmetric case to asymmetric case. To derive formulas, we investigate the corresponding integrals on self-similar measure and use the self-similarity of distance and measure. For simplicity, we introduce some systematic symbolic assignments and make some assumptions on the graph. We verify that our formulas are correct using the numerical calculation results.

中文翻译：

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替代树网络的偏心距离和

在本文中，我们研究了替代树网络的偏心距离和。偏心距和的计算自然会涉及到平均测地距离的计算，而且要复杂得多。我们得到了对称和非对称替换树网络的平均测地距离和偏心距离和的渐近公式。我们关于平均测地距离的结果概括了 [T. Li, K. Jiang 和 L. Xi，自相似分形树的平均距离，分形 26(1) (2018) 1850016.] 从对称情况到非对称情况。为了推导公式，我们研究了自相似测度上的相应积分，并使用距离和测度的自相似性。为简单起见，我们引入一些系统的符号赋值，并对图做一些假设。我们使用数值计算结果验证我们的公式是正确的。