*Topics and order are subject to changes as the semester evolves.*

#### I Networks & Graph Theory

- complex systems and networks
- graph representation, notation and definitions
- degree distribution, paths, distance distribution, diameter, connectedness
- application: social network analysis
- triadic closure, clustering coefficient
- strong and weak ties
- homophily and social-affiliation networks

- node centrality and importance
- network robustness and resilience

#### II Network Models

- small-world phenomenon
- random graph model (Erdös-Rényi graphs)
- Watts-Strogatz model
- rich-get-richer phenomenon
- fitness model, Barabási-Albért graphs, and scale-free networks

#### III Analyzing Networks: Graph Mining

- application: community detection
- betweenness
- Girvan-Newman algorithm
- graph clustering, graph partitioning

- triangles, cliques, and paths
- application: structure of the web & link analysis
- web graph
- hubs and authorities (HITs)
- PageRank

#### IV Modeling Dynamics: Information Cascades, Link Prediction, Epidemics

We can choose *some* topics to study in more detail (*time permitting*).

- information cascades, diffusion models: how does information spread?
- link prediction, supervised random walks: how do friendship suggestions work?
- epidemic models: how do diseases spread?

#### V (Machine) Learning with Graphs: Node and Graph Classification

We can choose *some* topics to study in more detail (*time permitting*).

- node similarity and node classification
- graph similarity and graph classification
- graph and node embeddings