Class Introduction to the Theory of Graphs and Networks

The course "Introduction to Graph Theory and Networks" aims to provide students with tools for using graphs in various problems. It starts with basic concepts, covers classical problems, and concludes with a brief introduction to complex networks and their applications in Data Science problems.

S1. Basic Concepts (Definition, vertices, edges, directed and undirected graphs, metrics, subgraphs, distance and connectivity, isomorphisms, invariants, and spectral theory).

S2. Networks and Flows (Maximum flow, minimum cost flow).

S3. Network Analysis (Network representation, visualization, degree, distance measures, and centrality).

S4. Random Graphs (Erdös-Rényi, Watts-Strogatz, Barabasi-Albert).

S5. Applications in Data Science.

There are theoretical and practical classes, being mainly expositives and in-person lectures. We expect at least 115 hours off class dedication and 52h to un-person classes.

TM1. Lectures.

TM2. Practical, incorporating both explanatory segments and exercises.

TM3. Theoretical and practical exercise assignments.

TM4. Independent project development.

TM5. Recommendation of supplementary materials.

• L. Barabasi, M. Pósfai, Network Science, Cambridge University Press, 2016
• B. Bollobás, Random Graphs, Cambridge University Press, 2001
• D. M. Cardoso, J. Szymanski, M. Rostami, Matemática Discreta: combinatória, teoria dos grafos e algoritmos, Escolar Editora, 2008.
• P. Feofiloff, Y. Kohayakawa, Y. Wakabayashi, Uma Introdução Sucinta à Teoria dos Grafos, 2004