Latest information:


Problem sets:

Problem set 1 (due Tue., May 07) —
Branching processes, random graphs and phase transitions, small-world model and routing, power laws and preferential attachment


Lecture notes:

Please note that scribed notes marked as 'preliminary' have not yet been edited throughly. In addition, be aware that notes may contain typos (e-mail me if you find one).

Lecture 01 (01/15/13) —
Introduction, small-world hypothesis, Landau symbols


Lecture 02 (01/17/13) —
Random graphs, branching processes


Lecture 03 (01/22/13) —
Branching processes (cont'd), Chernoff bounds


Lecture 04 (01/24/13) —
Erdős-Rényi model, threshold functions


Lecture 05 (01/29/13) —
Second-moment method, thresholds in Erdős-Rényi model


Lecture 06 (01/31/13) —
Giant component and connectivity


Lecture 07 (02/05/13) —
Configuration model, expander graphs, weak ties, clustering, Watts-Strogratz model


Lecture 08 (02/07/13) —
Decentralized routing, Kleinberg small-world model


Lecture 09 (02/12/13) —
Kleinberg small-world model (cont'd)


Lecture 10 (02/14/13) —
Introduction to power laws


Lecture 11 (02/19/13) —
Power laws (cont'd)


Lecture 12 (02/21/13) —
Preferential attachment models, Yule process


Lecture 13 (02/26/13) —
Node ranking, path metrics


Lecture 14 (02/28/13) —
Spectral metrics, PageRank


Lecture 15 (03/05/13) —
HITS algorithm, SALSA


Lecture 16 (03/07/13) —
Community detection, graph Laplacian


Lecture 17 (03/19/13) —
Spectral clustering, k-means algorithm


Lecture 18 (03/21/13) —
Cut measures, relaxation and spectral clustering


Lecture 19 (03/26/13) —
Spectral clustering (cont'd), relation to random walks


Lecture 20 (03/28/13) —
Modularity maximization


Lecture 21 (04/02/13) —
TBA


Lecture 22 (04/04/13) —
TBA


Lecture 23 (04/09/13) —
Mean-field models of epidemics


Lecture 24 (04/11/13) —
SIR and Reed-Frost model


Lecture 25 (04/16/13) —
Reed-Frost model (cont'd)


Lecture 26 (04/18/13) —
SIS and fast extinction


Lecture 27 (04/23/13) —
Innovation diffusion and threshold models


Lecture 28 (04/25/13) —
Contagion on graphs


Lecture 29 (04/20/13) —
General threshold and cascade models


Lecture 30 (05/02/13) —
Optimized epidemics and submodularity


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