T-79.7003 Graphs and Networks
General Information
Instructor: Charalampos E. Tsourakakis
Classroom: Lecture hall T5 (CS building)
Original Web page link: T-79.7003
Time: Fri 2-5pm
Email: tsourolampis at gmail dot com.
Grading
- 3 homeworks, 5% each (total 15%)
- 2 tests, 30% each (total 60%)
- 1 Project, 25%
Homework policy
You may discuss the problems with other students but you must write your solutions
on your own and list your collaborators. You may not search the Web for solutions.
You may consult outside materials, but you must cite your sources in your solutions.
Violation of the policy may result in receiving a zero grade for the question or the assignment or even the whole course. The penalty will be assessed at the instructor’s discretion.
Handouts
- Lecture 1 (Sep 13, 2013): introduction
- Lecture 2 (Sep 20, 2013): thresholds for K4s and graph connectivity
- Optional readings
- Colorful Triangle Counting and a MapReduce Implementation
This paper contains the analysis of a randomized triangle counting algorithm
which is based on the second moment method. - Cayley’s formula (ch. 26)
We used Cayley’s formula to upper bound the expected number of components of order k
in G(n,p). This book contains four beautiful proofs of the formula.
- Colorful Triangle Counting and a MapReduce Implementation
- Optional readings
-
- Lecture 3 (Sep 27, 2013): Phase transition
- HW1 is out
- Suggested papers are out
- Lecture slides (pdf)
- Readings
- Simulation video, the evolution of the G(n,p) random graph
- Lecture 3 (Sep 27, 2013): Phase transition
- Lecture 4 (Oct 4, 2013): Probabilistic tools and random graph applications I
- Readings
- Concentration (read Sections 1,2, pages 1-10)
- Readings
- Lecture 5 (Oct 11, 2013): Probabilistic tools and random graph applications II
- Readings
- Concentration (read Section 3, pages 10-26)
- Sharp concentration of the chromatic number on random graphs G(n,p)
- Optional Readings
- Readings
- Midterm exam (Oct. 18, 2013)
- Fall midterm break (Oct. 25, 2013)
- Lecture 6 (Nov 1, 2013): Properties and models of real-world networks. Degree sequence of preferential attachment
- Readings
- The degree sequence of a scale-free random graph process
- For a quick proof sketch check 4.1 from this book chapter.
- Navigation in a small world
- Collective dynamics of ‘small-world’ networks
- Suggested Readings
- CHKNS model
- For more on the compressibility of the Web graph, read the paper Models for the Compressible Web and slides by Ravi Kumar on the above paper
- For an alternative way of obtaining degree sequences which follow a power law, read the paper Heuristically optimized trade-offs: A new paradigm for power laws in the Internet
- Readings
- Lecture 7 (Nov 8, 2013): Random Walks on Graphs
- Lecture 8 (Nov 15, 2013): Spectral Clustering, Cheeger’s inequality
- Lecture notes, Chapter 1 from Grimmett’s book (pdf) (cont.)
- KDD’13 Tutorial (slides 133-176)
- Readings
- Cheeger’s inequality I, Cheeger’s inequality II (Dan Spielman’s notes)
- Lecture 9 (Nov 22, 2013): One hour guest lecture on boostrap percolation by Dr. Thomas Vallier + project presentations
- Bootstrap percolation on G(n,p)
- Slides by Thomas Vallier
- Project Presentations
- Orestis
- Hristo
- Miquel
- Abdulmelik
- Lecture 10 (Nov 29, 2013): Project presentations
- Geraud, Louiza, Sanja
- Eric, Emanuelle
- Ehsan
- Polina
- HW3 is out
- Finland’s Independence Day (Dec 6, 2013)
- Lecture 11 (Dec 13, 2013): Various topics
- Readings
- Chapters 3,6 and 8 from Mathematical and Algorithmic Analysis of Network and Biological Data
- Spectral Sparsification of Graphs by Nikhil Srivastava
- Spectral Sparsification of Graphs and Approximations of Matrices I by Daniel Spielman
- Spectral Sparsification of Graphs and Approximations of Matrices II by Daniel Spielman
- Readings
Data Sources
Colorado Index of Complex Networks
Stanford Large Network Dataset Collection (SNAP)
The University of Florida Sparse Matrix Collection (UFS)
Twitter graph (2009)
Software, Libraries
NetworkX (Python)
JUNG (Java)
Stanford Large Network Analysis (SNAP system) (C++, Jure Leskovec)
MATLAB BGL (Matlab, David Gleich)
Mathematica, Graph and Network Modeling (Mathematica)
Visualization software
Related Web pages
David Aldous (Berkeley)
Easly-Kleinberg (Cornell)
Dan Spielman (Yale)
Aaron Clauset (UC Boulder)
Books, Notes
Rick Durrett’s book
Networks, Crowds, and Markets: Reasoning About a Highly Connected World
Remco Van Der Hofstad’s notes
Alan Frieze’s notes (handwritten)
Suggested papers
A list of suggested papers follows. I have grouped the papers by category to facilitate your search, but it is worth outlining that some papers could belong to more than one category.
Stochastic graph models
-
- A geometric preferential attachment model of networks
A. Flaxman, A. Frieze, J. Vera - Affiliation networks
S. Lattanzi and D. Sivakumar - The Diameter of a Scale-free Random Graph
B. Bollobas, O. Riordan - A General Model of Web Graphs
C. Cooper, A. Frieze - First to Market is not Everything: an Analysis of Preferential Attachment with Fitness
C. Borgs, J. Chayes, C. Daskalakis, S. Roch - Estimating and Understanding Exponential Random Graph Models
S. Chatterjee, P. Diaconis - Graph Evolution: Densification and Shrinking Diameter
J. Leskovec, J. Kleinberg, C. Faloutsos - Stochastic Kronecker graphs
M. Mahdian, Y. Xu - A Random Graph Model for Power Law Graphs
W. Aiello, F. Chung, L. Lu - The Diameter of Sparse Random Graphs
Fan Chung, Linyuan Lu - Stochastic models for the web graph (ps)
R. Kumar, P. Raghavan, S. Rajagopalan, D. Sivakumar, A. Tomkins, E. Upfal - Models for the Compressible Web
Flavio Chierichetti, Ravi Kumar, Silvio Lattanzi, Alessandro Panconesi, and Prabhakar Raghavan - The Diameter of random power law graphs
Linyuan Lu
- A geometric preferential attachment model of networks
Estimating models from network data
-
- Winners don”t take all: Characterizing the competition for links on the Web
Pennock, D. M., Flake, G. W., Lawrence, S., Glover, E. J., and Giles, C. L. - Moment based estimation of stochastic Kronecker graph parameters
David F. Gleich and Art B. Owen - Kronecker graphs: An approach to modeling networks
Jure Leskovec, Deepayan Chakrabarti, Jon Kleinberg, Christos Faloutsos, Zoubin Ghahramani
- Winners don”t take all: Characterizing the competition for links on the Web
Strategic graph models
-
- Anarchy is free in network creation
R. Graham, L. Hamilton, A. Levavi, P.-S. Loh - The Price of Anarchy in Network Creation Games
E. Demaine, M. Hajiaghayi, H. Mahini, M. Zadimoghaddam - On a network creation game
A. Fabrikant, A. Luthra, E. Maneva, C. Papadimitriou, and S. Shenker.
Check also these - A Strategic Model of Social and Economic Networks
M. Jackson, A. Wolinsky
- Anarchy is free in network creation
Diffusion related (rumor spreading, cascades, network reconstruction etc.)
-
- Rumor Spreading in Social Networks.
F. Chierichetti, S. Lattanzi and A. Panconesi - Trace Complexity of Network Inference
B. Abrahao, F. Chierichetti, R. Kleinberg, and A. Panconesi - Inferring Networks of Diffusion and Influence
M. Gomez-Rodriguez, J. Leskovec, A. Krause - Modeling Information Propagation with Survival Theory
Manuel Gomez Rodriguez, Jure Leskovec, Bernhard Schölkopf - Spotting Culprits in Epidemics: How many and Which ones?
B. A. Aditya, J. Vrekeen, C. Faloutsos - Rumors in a Network: Who’s the Culprit?
Devavrat Shah, Tauhid Zaman - Information Cascade at Group Scale
M. Eftekhar, Y. Ganjali, N. Koudas - Randomized Rumor Spreading
R. Karp, C. Schindelhauer, S. Shenker, B. Vöcking
- Rumor Spreading in Social Networks.
Social learning
-
- Dynamics of information exchange in endogenous social networks
Daron Acemoglu, Kostas Bimpikis, Asuman Ozdaglar - Bayesian learning in social networks
Daron Acemoglu, Munther Dahleh, Ilan Lobel, Asuman Ozdaglar
Check this out too.
- Dynamics of information exchange in endogenous social networks
Subgraphs
-
- Counting Arbitrary Subgraphs in Data Streams
Daniel M. Kane, Kurt Mehlhorn, Thomas Sauerwald, and He Sun - Triangle counting in dynamic graph streams
K. Kutzkov, R. Pagh - On the Streaming Complexity of Computing Local Clustering Coefficients
K. Kutzkov, R. Pagh - Efficient Triangle Counting in Large Graphs via Degree-based Vertex Partitioning
Mihail N. Kolountzakis, Gary L. Miller, CET, Richard Peng - Counting Triangles in Data Streams
L. Buriol, G. Frahling, S. Leonardi, A. Marchetti-Spaccamela, C. Sohler - Subgraph Frequencies: Mapping the Empirical and Extremal Geography of Large Graph Collections
J. Ugander, L. Backstrom, J. Kleinberg - Counting Stars and Other Small Subgraphs in Sublinear Time
Mira Gonen, Dana Ron, Yuval Shavitt
Check this nice talk on sublinear algorithms and property testing here.
- Counting Arbitrary Subgraphs in Data Streams
Dense subgraphs and graph partitioning
-
- A Local Algorithm for Finding Well-Connected Clusters
Zeyuan A. Zhu, Silvio Lattanzi and Vahab Mirrokni - Streaming Balanced Graph Partitioning for Random Graphs
Isabelle Stanton - Spectral Partitioning of Random Graphs
Frank McSherry - Statistical Properties of Community Structure in Large Social and Information Networks
Jure Leskovec, Kevin Lang, Anirban Dasgupta, Michael Mahoney - On finding dense subgraphs
Samir Khuller and Barna Saha - Local Graph Partitioning using PageRank Vectors
R. Andersen, F. Chung, K. Lang - Balanced label propagation for partitioning massive graphs
Johan Ugander, Lars Backstrom
- A Local Algorithm for Finding Well-Connected Clusters
Evolutionary dynamics on graphs
-
- Evolutionary dynamics on graphs and the Supplement
E. Lieberman, C. Hauert, M. Nowak - Natural models for evolution on networks.
G.B. Mertzios, S. Nikoletseas, C. Raptopoulos, P.G. Spirakis - Approximating fixation probabilities in the generalized Moran process
J. Diaz, L.A. Goldberg, G.B. Mertzios, D. Richerby, M. Serna, and P.G. Spirakis
- Evolutionary dynamics on graphs and the Supplement
Learning
-
- Learning from labeled and unlabeled data on a directed graph
D. Zhou, J. Huang, B. Schoelkopf - Fitting a graph to vector data
S. Daitch, J. Kelner, D. Spielman - Fast Random Walk with Restart and Its Applications
H. Tong, C. Faloutsos, J. Pan - Learning from labeled and unlabeled data using graph mincuts
A. Blum, S. Chawla - The Fastest Mixing Markov Process on a Graph and a Connection to a Maximum Variance Unfolding Problem
J. Sun, S. Boyd, L. Xiao, and P. Diaconis
or/and a related NIPS paper
Colored Maximum Variance Unfolding
L. Song, A. Smola, K. Borgwardt, A. Gretton
- Learning from labeled and unlabeled data on a directed graph
Various
- On the Bias of Traceroute Sampling: or, Power-Law Degree Distributions in Regular Graphs
D. Achlioptas, A. Clauset, D. Kempe, C. Moore - Trading in Networks: Theory and Experiment
S. Choi, A. Galeotti, S. Goyal - The Network Origins of Large Economic Downturns
D. Acemoglu, A. Ozdaglar, A. Tahbaz-Salehi - A Random Graph Model of Multi-Hospital Kidney Exchanges
Panos Toulis, David Parkes - Suppressing cascades of load in interdependent networks
Charles D. Brummitt, Raissa M. D’Souza, and E. A. Leicht - Maximum Matchings in Random Bipartite Graphs and the Space Utilization of Cuckoo Hash Tables
Alan Frieze, Pall Melsted
A nice overview of cuckoo hashing and related results is presented in this thesis
Random Bipartite Graphs and their Application to Cuckoo Hashing
R. Kutzelnigg - The Spread of Evidence-Poor Medicine via Flawed Social-Network Analysis
R. Lyons
[Of course in order to be able to understand the critique you also need to read the referred work of Christakis and Fowler]
Note
You are not obliged to pick one of the aforementioned papers. You can choose a paper of your own preference as long as it is related to the content of the class. Some conferences and journals where you can search for more papers follow.
- ACM Conference on Electronic Commerce (EC)
- KDD
- WWW
- WSDM
- ESA
- ICALP
- SODA
- Random structures and algorithms (RSA)
- Combinatorics, Probability and Computing (CPC)
- Internet Mathematics