Course Overview
General Info:
Instructor: Fragkiskos Malliaros
Email: fragkiskos.me [at] gmail.com
Office hours: Please send me an email or contact me on Teams
TA: Alexandre Duval
Email: alexandre.duval [at] centralesupelec.fr
Edunao: centralesupelec.edunao.com
Networks (or graphs) have become ubiquitous as data from diverse disciplines can naturally be mapped to graph structures. Social networks, such as academic collaboration networks and interaction networks over online social networking applications are used to represent and model the social ties among individuals. Information networks, including the hyperlink structure of the Web and blog networks, have become crucial mediums for information dissemination, offering an effective way to represent content and navigate through it. A plethora of technological networks, including the Internet, power grids, telephone networks and road networks are an important part of everyday life. The problem of extracting meaningful information from large scale graph data in an efficient and effective way has become crucial and challenging with several important applications and towards this end, graph mining and analysis methods constitute prominent tools. The goal of this course is to present recent and state-of-the-art methods and algorithms for analyzing, mining and learning large-scale graph data, as well as their practical applications in various domains (e.g., the web, social networks, recommender systems).
Schedule and Lectures
The topics of the lectures are subject to change (the following schedule outlines the topics that will be covered in the course). The slides for each lecture will be posted on
Edunao just before the start of the class.
The due dates of the assignments/project are subject to change.
| Week |
Date |
Topic |
Material |
Assignments/Project |
| 1 | March 1 |
○ Introduction to network science and machine learning on graphs
○ Basic network properties; the random graph and small-world models
|
Lecture 1A
Lecture 1B
| |
| 2 | March 8 |
○ Power-law degree distribution and the Preferential Attachment model
○ Centrality criteria and link analysis algorithms
○ Practical session
|
Lecture 2A
Lecture 2B
| |
| 3 | March 15 |
○ Link prediction and graph similarity
○ Graph similarity
○ Practical session (preparation for the Kaggle challenge)
|
Lecture 3A
Lecture 3B
| Data challenge out
|
| 4 | March 19 |
○ Representation learning on graphs; node embedding models
○ Practical session
|
Lecture 4
| Project proposal due on March 21 |
| 5 | March 22 |
○ Graph neural networks
○ Practical session
|
Lecture 5
| |
| 6 | March 26 |
○ Graph clustering and community detection
○ Practical session
| Lecture 6 | |
| 7 | April 2 |
○ Cascading behavior in networks; Influence maximization
○ Practical session
|
Lecture 7
| Data challenge due on April 4 |
| 8 | April 9 | Project presentations | | Project final report due on April 9
Online poster session or presentations
|
[March 1] Lecture 1: Introduction; basic network properties; generative models
Part A: Introduction to network science and machine learning on graphs
Introduction to graph mining, network analysis, and machine learning on graphs; administrivia, course structure and overview of the topics that will be covered in the course.
Reading:
Part B: Basic network properties; the random graph and small-world models
Presentation of basic concepts in graph theory, linear algebra and spectral graph theory that will be used throughout the course. Basic network properties: degree distribution, clustering coefficient and shortest path length. The Erdos-Renyi random graph model and its basic properties. Comparison to the properties of real networks. The small-world phenomenon and the small-world model.
Reading:
Additional:
- Networks: An Introduction (Chapters 6, 8 and 9)
- SVD and Low Rank Matrix Approximations, lecture notes by Tim Roughgarden and Gregory Valiant (Stanford University)
- Lectures on Spectral Graph Theory, by Fan Chung (Chapter 2: Eigenvalues and the Laplacian of a graph)
- J. Leskovec and E. Horvitz. Planetary-Scale Views on a Large Instant-Messaging Network. In WWW, 2008
- Lecture 3, Lecture 4 and Lecture 5 from CSE 258 (background knowledge in data mining and machine learning)
- Random graphs, lecture notes by Aaron Clauset (CU Boulder)
- Diameter on d-regular random graphs, lecture notes by Yaron Singer (Harvard University)
- Networks: An Introduction (Chapter 12)
- P. Erdos and A. Renyi. On Random Graphs I. Publicationes Mathematicae (6) 290-297, 1959
- P. Erdos and A. Renyi. On the evolution of random graphs. Magyar Tud. Akad. Mat. Kutato Int. Koezl., 1960
- D. J. Watts and S. H. Strogatz. Collective dynamics of 'small-world' networks. Nature 393:440-42, 1998
- P. S. Dodds, R. Muhamad, D. J. Watts. An Experimental Study of Search in Global Social Networks. Science 301, 2003
- D. J. Watts, P. S. Dodds, M. E. J. Newman. Identity and Search in Social Networks. Science, 296, 1302-1305, 2002
- M. E. J. Newman. Models of the Small World: A Review., J. Stat. Physics 2000
- J. Kleinberg. The small-world phenomenon: An algorithmic perspective. Proc. ACM Symposium on Theory of Computing, 2000
- L. Backstrom, P. Boldi, M. Rosa, J. Ugander, and S. Vigna. Four Degrees of Separation. ACM Web Science Conference. 2012
- J. Ugander, B. Karrer, L. Backstrom, and C. Marlow. The Anatomy of the Facebook Social Graph. arXiv, 2012
[March 8] Lecture 2: The Preferential Attachment model; centrality criteria
Part A: Power-law degree distribution and the Preferential Attachment model
Power-law degree distribution in real networks. The Preferential Attachment model. Consequences of skewed degree distribution in the robustness of real networks.
Reading:
Additional:
- A. Clauset, C.R. Shalizi, and M.E.J. Newman. Power-law distributions in empirical data. SIAM Review 51(4), 661-703, 2009
- Networks, crowds, and markets (Chapter 18)
- Graph Mining: Laws, Tools, and Case Studies (Chapter 2 and 9)
- Bela Bollobas, Oliver Riordan, Joel Spencer and Gabor Tusnady. The degree sequence of a scale-free random graph process. Journal Random Structures and Algorithms 18(3), 2001
- M. Mitzenmacher. A Brief History of Generative Models for Power Law and Lognormal Distributions. Internet Mathematics 1(2), pp. 226-251, 2004
- M. Faloutsos, P. Faloutsos, C. Faloutsos. On Power-Law Relationships of the Internet Topology. In SIGCOMM, 1999.
- R. Albert, H Jeong, and A.-L. Barabasi. The diameter of the world wide web. Nature 401, 130-131, 1999
- A.L Barabasi, R. Albert. Emergence of scaling in random networks. Science, 286, 1999
- J. Leskovec, J. Kleinberg, and C. Faloutsos. Graph Evolution: Densification and Shrinking Diameters. ACM TKDD, 2007
- J. Leskovec, D. Chakrabarti, J. Kleinberg, C. Faloutsos, and Z. Ghahramani. Kronecker Graphs: An approach to modeling networks. Journal of Machine Learning Research (JMLR) 11:985-1042, 2010
Part B: Centrality criteria and link analysis algorithms
Centrality criteria in graphs (degree, closeness, betweenness, eigenvector, Katz). Link analysis ranking algorithms (HITS and PageRank).
Reading:
Additional:
- Networks: An Introduction (Chapter 7, Sections 7.1 - 7.7)
- F. Bonchi, G. De Francisci Morales, and M. Riondato. Centrality Measures on Big Graphs: Exact, Approximated, and Distributed Algorithms. Tutorial at WWW, 2016.
- U Brandes. A faster algorithm for betweenness centrality. Journal of Mathematical Sociology 25(2), 163-177, 2001
- T. H. Haveliwala. Topic-Sensitive PageRank. In Proc 11th International World Wide Web Conference, 2002
- G. Jeh and J. Widom. Scaling Personalized Web Search. In Proc. roceedings of the 12th international conference on World Wide Web (WWW), 2003
- A. Borodin, J. S. Rosenthal, G. O. Roberts, and P. Tsaparas. Finding Authorities and Hubs From Link Structures on the World Wide Web. In Proc. 10th International World Wide Web Conference, 2001
- P. Berkhin. A Survey on PageRank Computing. Internet Mathematics 2(1), pages 73-120, 2005
Graph similarity. Graph kernels.
Reading:
Additional:
- P. Papadimitriou, A. Dasdan and H. Garcia-Molina. Web Graph Similarity for Anomaly Detection. Journal of Internet Services and Applications 1(1), pp. 19-30, 2010
- S. Soundarajan, T. Eliassi-Rad, and B. Gallagher. A Guide to Selecting a Network Similarity Method. In SDM, 2014
- K. M. Borgwardt and H. Kriegel. Shortest-path kernels on graphs. In ICDM, 2005
- N. Shervashidze, T. Petri, K. Mehlhorn, K. M. Borgwardt, and S. Vishwanathan. Efficient Graphlet Kernels for Large Graph Comparison. In AISTATS, 2009
- T. Gartner, P. Flach, and S. Wrobel. On Graph Kernels: Hardness Results and Efficient Alternatives. Learning Theory and Kernel Machines, 2003
- X. Gao, B. Xiao, D. Tao, and X. Li. A survey of graph edit distance. Pattern Analysis and Applications 13(1), 113-129, 2010
- R.C. Wilson and P. Zhu. A Study of Graph Spectra for Comparing Graphs and Trees. Journal of Pattern Recognition 41(9), 2833-2841, 2008
[March 19] Lecture 4: Representation learning on graphs
Methods for learning node embeddings on graphs (LINE, DeepWalk and node2vec).
Reading:
- J. Tang, M. Qu, M. Wang, M. Zhang, J. Yan, and Q. Mei. LINE: Large-scale information network embedding. In WWW, 2015
- B. Perozzi, R. Al-Rfou, and S. Skiena. DeepWalk: Online Learning of Social Representations. In KDD, 2014
- A. Grover and J. Leskovec. node2vec: Scalable Feature Learning for Networks. In KDD, 2016
Additional:
- J. B. Tenenbaum, V. De Silva, and J. C. Langford. A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science, 290:5500, pp. 2319-2323, 2000
- S. T. Roweis and L. K. Saul. Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science, 290:5500, pp. 2323-2326, 2000
- M. Belkin and P. Niyogi. Laplacian eigenmaps and spectral techniques for embedding and clustering. In NIPS, 2001
- T. Mikolov, K. Chen, G. Corrado, and J. Dean. Efficient estimation of word representations in vector space. arXiv, 2013
- T. Mikolov, I. Sutskever, K. Chen, G.S. Corrado, and J. Dean. Distributed representations of words and phrases and their compositionality. In NIPS, 2013
- S. Cao, W. Lu, and Q. Xu. GraRep: Learning Graph Representations with global structural information. In CIKM, 2015
- S. Cao, W. Lu, and Q. Xu. Deep Neural Networks for Learning Graph Representations. In AAAI, 2016
- W. L. Hamilton, R. Ying, and J. Leskovec. Representation Learning on Graphs: Methods and Applications. IEEE Data Engineering Bulletin, 2017
- P. Goyal and E. Ferrara. Graph Embedding Techniques, Applications, and Performance: A Survey. arXiv, 2017
- A. Narayanan, M. Chandramohan, L. Chen, Y. Liu, and S. Saminathan. subgraph2vec: Learning Distributed Representations of Rooted Sub-graphs from Large Graphs. In KDD (MLG Workshop), 2016
- M. Niepert, M. Ahmed, and K. Kutzkov. Learning Convolutional Neural Networks for Graphs. In ICML, 2016
[March 22] Lecture 5: Graph neural networks
GNN models. Message aggregation strategies. Graph Convolutional Networks. GraphSAGE. Graph Attention Networks. Unsupervised and supervised training. Predictions (node-level, edge-level, graph-level) with GNNs.
Reading:
Additional:
- T. Kipf and M. Welling. Semi-Supervised Classification with Graph Convolutional Networks. In ICLR, 2017
- W.L. Hamilton, R. Ying, and J. Leskovec. Inductive Representation Learning on Large Graphs. In NIPS, 2017
- P. Veličković, G. Cucurull, A. Casanova, A. Romero, P. Liò, and Y. Bengio. Graph Attention Networks. In ICLR, 2018
[March 26] Lecture 6: Graph clustering and community detection
Community detection in networks. Girvan-Newman algorithm. Modularity and modularity optimization (greedy, spectral, Louvain method). Spectral clustering. Community evaluation criteria. Community detection in directed networks. Overlapping community detection. Community structure of large scale networks.
Reading:
- M. Girvan and M.E.J. Newman. Community structure in social and biological networks. PNAS 99, 2002
- M.E.J. Newman. Modularity and community structure in networks. PNAS, 2006
- U. von Luxburg. Tutorial on spectral clustering. Statistics and Computing 17(4), 2007
- Networks: An Introduction (Sections 11.5, 11.6)
- G. Palla, I. Derenyi, I. Farkas, T. Vicsek. Uncovering the overlapping community structure of complex networks in nature and society. Nature 435, 814-818, 2005
- J. Leskovec, K. Lang, A. Dasgupta, M. Mahoney. Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters. Internet Mathematics, 2009
Additional:
- J.-P. Onnela, J. Saramaki, J. Hyvonen, G. Szabo, D. Lazer, K. Kaski, J. Kertesz, A.L. Barabasi. Structure and tie strengths in mobile communication networks. PNAS, 2007
- M.E.J. Newman, M. Girvan. Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113, 2004
- A. Clauset, M.E.J. Newman, C. Moore. Finding community structure in very large networks. Phys. Rev. E 70, 066111, 2004
- V. D. Blondel, J.-L. Guillaume, R. Lambiotte, and E. Lefebvre. Fast unfolding of communities in large networks. Journal of statistical mechanics: theory and experiment, 2008
- S. Fortunato. Community detection in graphs. Physics Reports, 2010
- Social media mining (Chapters 6)
- U. Brandes, D. Delling, M. Gaertler, R. Gorke, M. Hoefer, Z. Nikoloski, and D. Wagner. On Modularity Clustering. IEEE TKDE 20(2), 2008
- S. Fortunato and S. Barthelemy. Resolution limit in community detection. Proc. Natl. Acad. Sci., 2007
- L. Backstrom, D. Huttenlocher, J. Kleinberg, X. Lan. Group Formation in Large Social Networks: Membership, Growth, and Evolution. In Proc. KDD, 2006
- J. Yang and J. Leskovec. Defining and Evaluating Network Communities based on Ground-Truth. In ICDM, 2012
- S. Fortunato. Community detection in graphs. Physics Reports, 2010
- Social media mining (Chapters 6)
- J. Shi and J. Malik. Normalized Cuts and Image Segmentation. IEEE Transactions on Pattern Analysis And Machine Intelligence, vol. 22, no. 8, 2000
- A. Ng, M. Jordan, and Y. Weiss. On spectral clustering: analysis and an algorithm . In NIPS, 2001
- F. D. Malliaros and M. Vazirgiannis. Clustering and Community Detection in Directed Networks: A Survey. Physics Reports, 533(4): 95-142, 2013
[April 2] Lecture 7A: Cascading behavior in networks
Cascading behavior. Models of virus and information probagation.
Reading:
Additional:
- Networks: An Introduction (Chapter 17: 17.1 - 17.4)
- Network science (Chapter 10)
- D. Chakrabarti, Y. Wang, C. Wang, J. Leskovec, and C. Faloutsos. Epidemic thresholds in real networks. ACM Trans. Inf. Syst. Secur. 10(4): 1:1-1:26, 2008
- B.A. Prakash, D. Chakrabarti, N.C. Valler, M. Faloutsos, and C. Faloutsos. Threshold conditions for arbitrary cascade models on arbitrary networks. Knowledge and Information Systems 33 (3), 2012
- M. Goetz, J. Leskovec, M. Mcglohon, and C. Faloutsos. Modeling blog dynamics. In ICWSM, 2009
- E. Adar and L. Adamic. Tracking information epidemics in blogspace. In Web Intelligence, 2005
- J. Ugander, L. Backstrom, C. Marlow, and J. Kleinberg. Structural Diversity in Social Contagion. PNAS 109 (16), 2012
- A. Goyal, F. Bonchi, and L.V.S. Lakshmanan. Learning influence probabilities in social networks. In WSDM, 2010
[April 2] Lecture 7B: Influence maximization
Influence maximization in social networks. The Greedy algorithm. Outbreak detection in networks.
Reading:
- D. Kempe, J. Kleinberg, and E. Tardos. Maximizing the Spread of Influence through a Social Network. In KDD, 2003
- M. Kitsak, L. K. Gallos, S. Havlin, F. Liljeros, L. Muchnik, H. E. Stanley, and H. A. Makse. Identification of influential spreaders in complex networks. Nature Physics 6, 888-893, 2010
Additional:
- A. Goyal, W. Lu, and L. S.V. Lakshmanan. SIMPATH: An Efficient Algorithm for Influence Maximization under the Linear Threshold Model. In ICDM, 2011
- J. Leskovec, A. Krause, C. Guestrin, C. Faloutsos, J. VanBriesen, and N. Glance. Cost-effective Outbreak Detection in Networks. In KDD, 2007
- W. Chen, Y. Wang, and S. Yang. Efficient Influence Maximization in Social Networks. In KDD, 2009
- W. Chen, Y. Yuan, and L. Zhang. Scalable Influence Maximization in Social Networks under the Linear Threshold Model. In ICDM, 2010
- A. Goyal, W. Lu, and L. V.S. Lakshmanan. CELF++: optimizing the greedy algorithm for influence maximization in social networks. In WWW, 2011
- E. Cohen, D. Delling, T. Pajor, and R.F. Werneck. Sketch-based Influence Maximization and Computation: Scaling up with Guarantees. In CIKM, 2014
- Y. Wang, G. Cong, G. Song, and K. Xie. Community-based greedy algorithm for mining top-K influential nodes in mobile social networks. In KDD, 2010
- M. Richardson and P. Domingos. Mining the Network Value of Customers. In KDD, 2001
- M. Richardson and P. Domingos. Mining Knowledge-Sharing Sites for Viral Marketing. In KDD, 2002
- J. Leskovec, L. Adamic, and B. Huberman. The Dynamics of Viral Marketing. TWEB, 2007
- A. Goyal, F. Bonchi, and K. V.S. Lakshmanan. A Data-Based approach to Social Influence Maximization. In PVLDB, 2012
Course Structure
Learning objectives
The course aims to introduce students to the field of graph mining and network analysis by:
- Covering a wide range of topics, methodologies and related applications.
- Giving the students the opportunity to obtain hands-on experience on dealing with graph data and graph mining tasks.
We expect that by the end of the course, the students will have a thorough understanding of various graph mining and learning tasks, will be able to analyze large-scale graph data as well as to formulate and solve problems that involve graph structures.
Prerequisites
There is no official prerequisite for this course. However, the students are expected to:
- Have basic knowledge of graph theory and linear algebra.
- Be familiar with fundamental data mining and machine learning tasks.
- Be familiar with at least one programming language (e.g., Python or any language of their preference).
During the first lecture, we will review basic concepts in graph theory, linear algebra and machine learning.
Reading material
Most of the material of the course is based on research articles. Some of the topics are also covered by the following books:
- David Easley and Jon Kleinberg. Networks, Crowds, and Markets. Cambridge University Press, 2010.
- William L. Hamilton. Graph Representation Learning. Morgan and Claypool Publishers, 2020.
- Mark E.J. Newman. Networks: An Introduction. Oxford University Press, 2010.
- Deepayan Chakrabarti and Christos Faloutsos. Graph Mining: Laws, Tools, and Case Studies. Synthesis Lectures on Data Mining and Knowledge Discovery, Morgan and Claypool Publishers, 2012.
- Reza Zafarani, Mohammad Ali Abbasi and Huan Liu. Social Media Mining. Cambridge University Press, 2014.
- Albert-Laszlo Barabasi. Network Science. Cambridge University Press, 2016.
Evaluation
The evaluation of the course will be based on the following:
- Data challenge this assignment aims to familiarize the students with basic graph mining and analysis tasks through a data challenge.
- Project: this will be the main component for the evaluation of the course. The students are expected to form groups of 3-4 people, propose a topic for their project, and submit a final project report (it would also be interesting to organize a poster session at the end of the quarter). Please, read the project section for more details.
The grading will be as follows:
| Data challenge (groups of 3-4 students): | 40% |
Project (groups of 3-4 students): | 60% |
Academic integrity
All of your work must be your own. Don't copy another student's assignment, in part or in total, and submit it as your own work. Acknowledge and cite source material in your papers or assignments.
Project
Details about the project of the course can be found on piazza.
Resources
Datasets
Software tools
- NetworkX: Python software package for graph analytics
- igraph: collection of software packages for graph theory and network analysis (Python, C++ and R)
- SNAP: high performance system for the analysis of large network (C++ and Python)
- Gephi: graph visualization and exploration software
Related conferences
Please find below a list of conferences related to the contents of the course (mostly in the field of data mining, social network analysis and the Web). We provide the DBLP website of each venue where you can access the proceedings (papers, tutorials, etc).
Check out the website of each conference (e.g.,
KDD 2016 ) for more information.