Graph Theory and Applications

The first part of the course will cover the basic elements of graph theory. It will provide the basic definitions, it will refer to the fundamental problems, and will present core graph analysis tools. Then, the course will cover more focused subjects of graph theory with broader interest, such as graph connectivity, coloring, coverage, matching Hamilton cycles, Euler cycles and planarity.

The second part of the course will focus on more modern applications from the field of complex network analysis with broader interest. It will present the structure and features of complex and social network graphs, such as random graphs, small-world graphs, power-law & scale-free graphs, regular graphs and random geometric graphs. Furthermore, the basic complex and social networks analysis tools will present, covering analysis metrics such as the node degree distribution, clustering coefficient, betweenness centrality, etc., and preferential analysis and evolution of networks. Finally, the basic community detection techniques will be presented.

Throughout the course, the students will be supported with sessions focusing on solving exercises and using available software tools & open data from social and other networks, in order to get exposed to practical network analysis and the study of graph properties