Course content In the first half of the semester, I plan to introduce dynamics of the complex networks. This will mainly deal with (i) various graph generative models, (ii) simple link prediction methods and (iii) diffusion processes on networks. More specifically,

• Overview of network science in the context of real life networks, and limitations of classical graph theory to address them.
• Generative models on graphs: Classical (physics based) random graph generative models - Price model, Barabasi Albert model and Erdos-Renyl model, with their statistical properties and generating functions. Modern graph generative models - Kronecker and Forest Fire models. Inference of Kronecker graphs. Difference between Forest Fire and Price models
• Link prediction heuristics: Adamic adar, jaccard coefficients, supervised random walk
• Processes over networks: Classical information cascade models, epidemic processes and their application on viral marketing.

In the second half of the semester, I plan to introduce deep learning on graphs. In particular,

• Representation learning of graphs - Various node representation methods e.g. Node2Vec, LINE, DeepWalk.
• Inductive node representation methods - GraphSAGE and graph convolutional network
• Graph neural networks
• Deep generative models on graphs - variational autoencoder on graphs and generative adversarial networks on graphs.

References

• Newman, Mark Ed, Albert-L303241szl303263 Ed Barab303241si, and Duncan J. Watts. The structure and dynamics of networks. Princeton university press, 2006.
• Easley, David, and Jon Kleinberg. Networks, crowds, and markets. Vol. 8. Cambridge: Cambridge university press, 2010.
• Zhang, Ziwei, Peng Cui, and Wenwu Zhu. "Deep learning on graphs: A survey." arXiv preprint arXiv:1812.04202 (2018).
• Hamilton, William L., Rex Ying, and Jure Leskovec. "Representation learning on graphs: Methods and applications." arXiv preprint arXiv:1709.05584 (2017).