Graph mining has been playing a pivotal role in many disciplines, ranging from computer science, sociology, civil engineering, physics, economics, marketing, to biology, life science, management science, political science, etc. Among others, a common and fundamental property of the graphs arising from these domains is connectivity. The goal of this tutorial is to (1) provide a concise review of the recent advances in optimizing graph connectivity and its applications; and (2) identify the open challenges and future trends. We believe this is an emerging, high-impact topic in graph mining, which will attract both researchers and practitioners in the big data research community. Our emphasis will be on (1) the recent emerging techniques on addressing graph connectivity optimization problem, especially in the context of big data; and (2) the open challenges/future trends, with a careful balance between the theories, algorithms and applications.
Introduction: Why Graphs and Why Graph Connectivity?
Part I: Graph Connectivity Measures
Part II: Graph Connectivity Optimization
Part III: Graph Connectivity Applications
Open Challenges and Future Directions