Complex Networks and Big Data

Aim

After completing the course the students should

• with adequate terminology, in a well-structured manner and logically coherent, be able to describe and conduct simpler calculations that relate to the specific concepts listed under "course contents".
• be able to describe, apply, and implement in a conventional programming language, and show engineering understanding of the theory and models used in the course.
• be able to, in a structured manner, and using adequate language and terminology, orally report computer laboratory work.

Content

Introduction to complex networks and network science. Graph representation of networks, adjacency matrix, degree sequence and degree distribution. Walks, paths and network motifs. Laplacian and its properties. Signed networks, bipartite, affiliation and tripartite networks. Similarity and clustering metrics. Centrality metrics, eigenvector centrality, Katz, PageRank, hubs and authorities. Sampling of networks, random walks, and friendship paradoxes. Assortativity metrics, modularity and degree correlations. Community detection and partitioning: Kernighan-Lin, Girvan-Newman and spectral algorithms. Network formation models: Poisson random networks, configuration model, preferential attachment, power-laws and scale-free networks, cutoffs. Watts-Strogatz model, Kleinberg model, small-world phenomena, searchability and reachability. Cascades, linear threshold models, DeGroot dynamic models and diffusion. Introduction to graph learning and graph signal processing.