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Description

Networks are discrete mathematical objects that describe systems of entities with pairwise relationship. Over the past several decades, technological advances in data collection and extraction have fueled an explosion of data in the form of networks from seemingly all corners of science. This course aims at providing the mathematical foundations of networks with a particular emphasis on their applications in modern data science, using tools from algorithmic graph theory and linear algebra. The topics include basic graph theory, network statistics, search algorithms, community detection, duality theorems and applications.

The course will utilize python (e.g., Networkx and Jupyter Notebook) to implement and test the techniques in graph theory and network science in synthetic and real data. Students are strongly encouraged to have some familarity in python prior to taking this course.

Much of the material covered can also be found in the following excellent texts:

• [GY] Graph Theory and Its Applications (Textbooks in Mathematics), Third Edition by Gross, Yellen, and Anderson
• [MFD] A first course in network science by Menczer, Fortunato, and Davis
• [E] Matrix Methods in Data Mining and Pattern Recognition, Second Edition by Elden

• [EEK] A first course in network theory by Estrada, Ernesto, and Knight
• [BHK] Foundations of data science by Blum, Hopcroft, and Kannan
• [EK] Networks, Crowds, and Markets: Reasoning about a Highly Connected World by Easley and Kleinberg
• [CZ] A First Course in Graph Theory by Chartrand and Zhang
• [KC] Statistical Analysis of Network Data with R (Use R!) 2nd ed. by Kolaczyk and Csardi
• [N] Network data repository

Lectures Notes

Will be available

Course Information