We present a method for graph clustering that is analogous with gradient ascent methods previously proposed for clustering points in space. We show that, when applied to a random geometric graph with data iid from some density with Morse regularity, the method is asymptotically consistent. Here, consistency is understood with respect to a density-level clustering defined by the partition of the support of the density induced by the basins of attraction of the density modes.

翻译：我们提出了一种图聚类方法，该方法与先前提出的用于空间点聚类的梯度上升方法类似。我们证明，当应用于数据独立同分布于具有莫尔斯正则性的某个密度的随机几何图时，该方法具有渐近一致性。这里的一致性，是相对于由密度模态的吸引域所诱导的密度支撑集划分所定义的密度水平聚类而言的。