The recent blossom of social network and communication services in both public and corporate settings have generated a staggering amount of network data of all kinds. Unlike the bio-networks and the chemical compound graph data often used in traditional network mining and analysis, the new network data grown out of these social applications are characterized by their rich attributes, high heterogeneity, enormous sizes and complex patterns of various semantic meanings, all of which have posed significant research challenges to the graph/network mining community. In this tutorial, we aim to examine some recent advances in network mining and analysis for social applications, covering a diverse collection of methodologies and applications from the perspectives of event, relationship, collaboration and network pattern. We would present the problem setting, the research challenges, the recent research advances and some future directions for each perspective.