Abstract: An interesting and important variant of data clustering is graph-clustering.On the one hand，the similarity between data objects in data set is often expressed by a graph.On the other hand，there is a growing interest in large complex network analysis.Further more，clustering can strengthen graphs’ visibility and contribute to visual analysis，observation and navigation.This paper explores to apply the max-min approach to clustering undirected and connected graphs without weights，and provides a new algorithm with the characteristics of simplicity，high efficiency and excellent fitness to clustering large static graphs.