Yanhua Li, Ph.D. Candidate in Computer Science, University of Minnesota, Twin Cities, USAComplex networks, including the Internet, wireless and cellular networks, and on-line social networks, are becoming indispensable parts of our daily lives. These networks arising from a wide range of applications can be represented and studied as graphs, and the underlying link patterns play an important role in understanding and solving problems in such applications. For example, many online social networks, such as Twitter and Google+, can be viewed as directed graphs with uni-directional "following'' relations among users, and the link directions contain crucial information about how users form social communities. In another application, online social networks such as Slashdot and Epinions represent relationships between users as links with positive or negative weights, which correspond to friend and foe relations. These networks are referred to as signed networks, where those signed links generate new challenges in understanding and studying the underlying network properties. In this talk, I present my work on developing theories for studying and characterizing various crucial graph properties, such as the edge directionality in directed graphs and the edge polarity in signed graphs. I do so by emphasizing on applications to detecting stable social communities and understanding social influence propagation patterns on online social networks.
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