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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix CHAPTER 1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Research Problem and Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.1 Issues in Finding an Appropriate Goodness Function . . . . . . . . . . . 3 1.2.2 Issues in Graph Computation . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 CHAPTER 2. Review of Literature . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1 Random Walk on Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Random Walk Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.2 Electric Current Based Measure . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Measures of Importance or Relative Importance on the Graphs . . . . . . . . . 9 2.2.1 Social Network Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.2 Link Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Connection Subgraph and its Recent Study . . . . . . . . . . . . . . . . . . . . 11 2.3.1 Candidate Subgraph Generation . . . . . . . . . . . . . . . . . . . . . . 11 2.3.2 Recent Studies Related to Connection Subgraph . . . . . . . . . . . . . 11

A two-stage strategy for solving the connection subgraph problem