In this paper, we introduce the concept of Edge Linking Coefficient(ELC), which is a value positively proportional to the number of the common neighbors shared by a pair of connected nodes and used as the measurement of the connection strength between them, and present a new divisive clustering algorithm for discovering communities hidden in large-scale complex networks based on it. Combining with the weak and the strong criteria of the communities, the ELCA method can effectively identify community structure in networks, which is shown in the experimental results on the synthetic and four real-world network data sets. In addition, the clustering algorithm is much faster than the GN algorithm and its variants, and suitable to the large-scale complex network clustering.