Mathematics for Data Science Probability Statistical Inference Programming in R Numerical Methods for Data Science Multivariate Statistics

The basic objectives of the subject are: 1. Understand the basics of networks, graphs, and families of graphs. Learn the concept of adjacency matrices and their significance. 2. Network Visualization: Gain proficiency in designing and visualizing networks. Explore techniques for decorating and handling large networks. 3. Descriptive Analysis of Networks: Analyze network structures through vertex and edge characteristics. Identify influential vertices, assess cohesion, detect communities, and understand assortativity. Explore real-world applications of network analysis. 4. Models and Inference for Networks: Familiarize with classical and generalized models for network representation. Study small world models and their applications. 5. Prediction in Networks: Learn methods for predicting network interactions using nearest neighbor approaches. Explore alternative prediction methods in network contexts.

1. Introduction and Preliminaries 1.1 Introduction 1.2 Examples of Networks 1.3 Graphs 2. Descriptive Analysis of Networks 2.1 Introduction 2.2 Network Visualization 2.3 Vertex Characteristics: Centrality, Hubs, Influencers,... 2.4 Edge Characteristics: Centrality 2.5 Network Cohesion 2.6 Community Detection in Networks 2.7 Assortativity 3. Models and Inference for Networks 3.1 Introduction 3.2 Mathematical Models for Networks 3.3 Statistical Models for Networks 4. Modeling and Prediction for Processes on Networks 4.1 Introduction 4.2 Nearest Neighbor Methods 4.3 Markov Random Fields 4.4 Kernel Methods

Learning activities: Theoretical classes Practical classes Tutorials Team work Individual work of the student In-person evaluation tests Methodology to be used: Theoretical classes with support material available on the Web. Problem solving classes. Computational practices in computer rooms. Oral exhibitions Tutorial regime: Individual tutorials throughout the course.