We propose a minimum span clustering (MSC) method for clustering and visualizing complex networks using the interrelationship of network components. To demonstrate this method, it is applied to classify the social science network in terms of aggregated journal-journal citation relations of the Institute of Scientific Information (ISI) Journal Citation Reports. This method of network classification is shown to be efficient, with a processing time that is linear to network size. The classification results provide an in-depth view of the network structure at various scales of resolution. For the social science network, there are 4 resolution scales, including 294 batches of journals at the highest scale, 65 categories of journals at the second, 15 research groups at the third scale, and 3 knowledge domains at the lowest resolution. By comparing the relatedness of journals within clusters, we show that our clustering method gives a better classification of social science journals than ISI's heuristic approach and hierarchical clustering. In combination with the minimum spanning tree approach and multi-dimensional scaling, MSC is also used to investigate the general structure of the network and construct a map of the social science network for visualization.