The objective of cluster analysis is to partition a set of data points into several groups based on a suitable distance measure. We first propose a model called local gravitation among data points. In this model, each data point is viewed as an object with mass, and associated with a local resultant force (LRF) generated by its neighbors. The motivation of this paper is that there exist distinct differences between the LRFs (including magnitudes and directions) of the data points close to the cluster centers and at the boundary of the clusters. To capture these differences efficiently, two new local measures named centrality and coordination are further investigated. Based on empirical observations, two new clustering methods called local gravitation clustering and communication with local agents are designed, and several test cases are conducted to verify their effectiveness. The experiments on synthetic data sets and real-world data sets indicate that both clustering approaches achieve good performance on most of the data sets.