For two dimensional surfaces (smooth) Ricci and Yamabe flows are equivalent. In 2003, Chow and Luo developed the theory of combinatorial Ricci flow for circle packing metrics on closed triangulated surfaces. In 2004, Luo developed a theory of discrete Yamabe flow for closed triangulated surfaces. He investigated the formation of singularities and convergence to a metric of constant curvature.

In this note we develop the theory of a naïve discrete Ricci flow and its modification — the so-called weighted Ricci flow. We prove that this flow has a rich family of first integrals and is equivalent to a certain modification of Luo’s discrete Yamabe flow. We investigate the types of singularities of solutions for these flows and discuss convergence to a metric of weighted constant curvature.

对于二维表面（光滑），Ricci 流和 Yamabe 流是等价的。2003 年，Chow 和 Luo 发展了封闭三角面上圆堆积度量的组合 Ricci 流理论。2004 年，罗发展了封闭三角面的离散 Yamabe 流理论。他研究了奇点的形成和收敛到常曲率度量。

在这篇文章中，我们发展了朴素离散 Ricci 流及其修改的理论——所谓的加权 Ricci 流。我们证明该流具有丰富的一阶积分族，相当于罗氏离散 Yamabe 流的某种修正。我们研究了这些流解的奇点类型，并讨论了收敛到加权常曲率度量的问题。