Wiener and Randić indices have long been studied in chemical graph theory as connection strength measures of graphs. Later, these indices were used in different fields such as network analysis. We consider two optimization problems related to these indices, with potential applications to network theory, in particular to epidemiological networks. Given a connected graph and a fixed total edge weight, we investigate how individual weights must be assigned to edges, minimizing the connection strength of the graph. In order to measure the connection strength, we use the weighted Wiener index and a modified version of the ordinary Randić index. Wiener index optimization is linear, while Randić index optimization turns out to be both nonlinear and nonconvex. Hence, we adopt the technique of separable programming to generate solutions. We present our experimental results by applying relevant algorithms to several graphs.

中文翻译：

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优化图的维纳和兰迪奇指数

在化学图论中，Wiener和Randić指数作为图的连接强度度量已被长期研究。后来，这些索引被用于网络分析等不同领域。我们考虑了与这些指标相关的两个优化问题，它们在网络理论（尤其是流行病学网络）中有潜在的应用。给定一个连接的图和固定的总边缘权重，我们研究如何将各个权重分配给边缘，从而最大程度地减小图的连接强度。为了测量连接强度，我们使用加权的Wiener指数和普通Randić指数的修改版本。维纳指数优化是线性的，而兰迪奇指数优化却是非线性和非凸的。因此，我们采用可分离编程的技术来生成解决方案。