Network Science
Department of Data Analysis and Artificial Intelligence,
School of Computer Science
National Research University Higher School of Economics
Winter - Spring 2022.
Instructors: Prof. Leonid Zhukov, Ilya Makarov
Course topics
- Statistical properties and modeling of networks
- Network structure and dynamics
- Processes on networks
- Predictions on networks (ML)
- Network embeddings (DL)
- Graph neural networks (DL)
Seminars/Labs
Module 3
Lectures
- [10.01.2022] Introduction to network science. [Lecture 1]
Introduction to the complex network theory. Network properties and metrics.
- [17.01.2022] Power law and scale-free networks.
[Lecture 2]
Power law distribution. Scale-free networks.Pareto distribution,
normalization, moments. Zipf law. Rank-frequency plot.
- [24.01.2022] Random graphs. [Lecture 3]
Erdos-Reni random graph model. Poisson and Bernulli
distributions. Distribution of node degrees. Phase transition,
gigantic connected component. Diameter and cluster
coefficient. Configuration model
- [31.01.2022] Network models [Lecture 4]
Barabasi-Albert model. Preferential attachement. Time evolition of node degrees. Node degree
distribution. Average path length and clustering coefficient. Small
world model. Watts-Strogats model. Transition from ragular to
random. Clustering coefficient and ave path lenght.
- [07.02.2022] Node centrality and ranking on networks. [Lecture 5]
Node centrality metrics, degree centrality, closeness centrality,
betweenness centrality, eigenvector centrality. Katz status index. Directed graphs. PageRank, Perron-Frobenius
theorem and algorithm convergence. Power iterations. Hubs and Authorites. HITS
algorithm.
- [14.02.2022] Structural properties of networks. [Lecture 6 ]
Structural and regular equivalence. Similarity metrics. Correlation coefficient and cosine similarity.
Assortative mixing and homophily. Modularity. Assortativity coefficient. Mixing by node degree. Assortative and disassortative networks. Cohesive subgroups. Graph cliques. k-cores decomposition.
- [21.02.2022] Graph partitioning. [Lecture 7]
Graph density. Graph pertitioning. Min cut, ratio cut, normalized and quotient cuts metrics. Spectral graph partitioning (normalized cut). Direct (spectral) modularity maximization. Multilevel recursive partitioning
- [28.02.2022] Network communities. [Lecture 8]
Network communities. Edge Betweenness. Newman-Girvin algorithm. Community detection algorithms. Overlapping communities. Clique percolation method. Heuristic methods. Fast community unfolding. Random walk based methods. Walktrap.
- [14.03.2022] Mathematical modeling of epidemics [Lecture 9]
Compartamental epidemic models: SI, SIS, SIR. Limiting cases. Basic reproduction number.
- [21.03.2022] Epidemics on networks [Lecture 10]
Spread of epidemics on network. SI, SIS, SIR network models. Epidemic threshold. Simulations of infection propagation on networks
Module 4
Lectures
- [04.04.2022] Cascades in networks and influence maximization [Lecture 11]
Cascades in netwroks. Difusion of innovatinon. Independent cascade model. Linear threshold model. Influence maximization.
Submodular functions. Finding most influential nodes in networks.
- [11.04.2020] Machine learning on graphs. Node classification [Lecture 12]
Node labeling. Label propagation. Iterative classification. Semi-supervised learning. Regularization on graphs
- [18.04.2020] Link prediction [Lecture 13]
Link prediction problem. Proximity measures. Scoring algorithms.
Prediction by supervised learning. Performance evaluation.
Additional reading material
Lecture 1:
- Albert-Laszlo Barabasi and Eric Bonabeau.
Scale
Free Networks. Scientific American, p 50-59, 2003
- Mark Newman.
The physics of networks. Physics Today,2008
-
Stanley Milgram. The Small-World Problem. Psychology
Today, Vol 1, No 1, pp 61-67, 1967
- J. Travers and S. Milgram.
An Experimental Study of the Small World
Problem. Sociometry, vol 32, No 4, pp 425-433, 1969
-
J. Leskovec and E. Horvitz. Planetary-Scale Views on a Large Instant-Messaging Network.
Proceedigs WWW 2008
-
L. Backstrom, P. Boldi, M. Rosa, J. Ugander, S. Vigna.
Four Degrees of Separation.
WebSci '12 Procs. 4th ACM Web Science Conference,
pp 33-42, 2012
Lecture 2:
-
M. E. J. Newman.
Power laws, Pareto distributions and Zipf’s law. Contemporary Physics 46(5), 323-351, 2005
- A. Clauset, C.R. Shalizi, M.E.J. Newman.
Power-law distributions in empirical data. SIAM Review 51(4), 661-703, 2009
-
M. Mitzenmacher.
A brief history of generative models for power law and lognormal
distributions. Internet Mathematics, vol 1, No. 2, pp. 226-251, 2004.
-
M.L. Goldstein, S.A. Morris, and G.G. Yen. Problems with fitting to
the power-law distribution , Eur. Phys. J. B 41, pp 255–258, 2004.
-
Chapter 18. Power Laws and
Rich-Get-Richer Phenomena. D. Easley and J. Kleinberg. "Networks, Crowds, and Markets: Reasoning About a Highly Connected
World".
Lecture 3:
- P. Erdos and A. Renyi.
On random graphs I. Publ. Math. Debrecen, 1959.
- P. Erdos and A. Renyi.
On the evolution of random graphs. Magyar Tud. Akad. Mat. Kutato Int. Koezl., 1960.
- Chapter 12. Random graphs. Mark Newman.
"Networks: An Introduction". Oxford University Press, 2010.
Lecture 4:
- Duncan J. Watts and Steven H. Strogatz.
Collective dynamics of ‘small-world’ networks.
. Nature 393:440-42, 1998.
- AL Barabasi and R. Albert.
Emergence of Scaling in Random Networks. Science, 286, 1999.
- Chapter 14. Models of network formation. Mark Newman.
"Networks: An Introduction". Oxford University Press, 2010.
-
Chapter 20. The Small-World
Phenomenon. D. Easley and J. Kleinberg. "Networks, Crowds, and Markets: Reasoning About a Highly Connected
World".
Lecture 5:
- Linton C. Freeman.
Centrality in Social Networks. Conceptual Clarification.
Social Networks, Vol 1, pp 215-239, 1978
- Phillip Bonacich.
Power and Centrality: A Family of Measures. American journal of sociology, Vol.92, pp 1170-1182, 1987.
- Leo Katz
A new status index derived from sociometric analysis . Psychometrika, 19, 39-43, 1953.
- Phillip Bonacich, Paulette Lloyd,
Eigenvector-like measures of centrality for asymmetric relations .
Social Networks 23, 191–201, 2001
- Chapter 7. Measures and metrics. Mark Newman.
"Networks: An Introduction". Oxford University Press, 2010.
- Chapter 5. Centrality and Prestige. S. Wasserman
and K. Faust.
"Social Network Analysis. Methods and Applications". Cambridge University Press, 1994
Lecture 6:
- Sergey Brin, Larry Page.
The Anatomy of a Large-Scale Hypertextual Web Search Engine,
,1998.
-
John M. Kleinberg.
Authoritative Sources in a Hyperlinked Environment. Proc. 9th ACM-SIAM Symposium on Discrete Algorithms, 1998.
-
Andrei Broder et all.
Graph structure in the Web. Procs of the 9th international World Wide Web conference,
2000
-
Amy N. Langville and Carl D. Meyer,
A Survey of Eigenvector Methods of Web Information Retrieval. 2004
-
David F. Gleich.
PageRank beyond the Web arXiv:1407.5107, 2014
- Chapter 7. Measures and metrics. Mark Newman.
"Networks: An Introduction". Oxford University Press, 2010.
-
Chapter 14. Link Analysis
and Web Search. D. Easley and J. Kleinberg. "Networks, Crowds, and Markets: Reasoning About a Highly Connected
World".
Lecture 7:
-
S. Borgatti, M. Everett. The class of all regular equivalences: algebraic structure
and computations. Social Networks, v 11, p65-68, 1989
-
E. A. Leicht, P.Holme, and M. E. J. Newman. Vertex similarity in networks. Phys. Rev. E 73, 026120, 200
-
G. Jeh and J. Widom. SimRank: A Measure of Structural-Context Similarity.
Proceedings of the eighth ACM SIGKDD , p 538-543. ACM Press, 2002
-
M. McPherson, L. Smith-Lovin, and
J. Cook. Birds of a Feather: Homophily in Social Networks, Annu. Rev. Sociol, 27:415-44, 2001.
- M. Newman.
Mixing patterns in
networks. Phys. Rev. E, Vol. 67, p 026126, 2003
-
M. D. Conover, J. Ratkiewicz, et al. Political Polarization on Twitter.
Fifth International AAAI Conference on Weblogs and Social Media, 2011
-
N. Christakis and J. Fowler. The spread of obesity in a large social network over 32 years. Engl J Med v 357:370-379, 2007
- Chapter 9. Structural Equivalence. S. Wasserman
and K. Faust.
"Social Network Analysis. Methods and Applications". Cambridge University Press, 1994
- Chapter 12. Network Positions and Roles. S. Wasserman
and K. Faust.
"Social Network Analysis. Methods and Applications". Cambridge University Press, 1994
- Chapter 7. Measures and metrics. Mark Newman.
"Networks: An Introduction". Oxford University Press, 2010.
Lecture 8:
- S. E. Schaeffer.
Graph
clustering. Comp. Sci. Rev., Vol. 1, p 27-64, 2007
- S. Fortunato.
Community detection in graphs . Physics Reports,
Vol. 486, pp. 75-174, 2010
-
V. Batagelj, M. Zaversnik.
An O(m) Algorithms for Cores
Decomposition of Networks. 2003
- M.E.J. Newman.
Modularity and community structure in networks. PNAS Vol. 103, N 23, pp 8577-8582, 2006
- Chapter 7. Matrix algorithms and graph partitioning. Mark Newman.
"Networks: An Introduction". Oxford University Press, 2010.
Lecture 9:
- H.W. Hethcote.
The Mathematics of Infections
Diseases. SIAM Review, Vol. 42, No. 4, pp. 599-653, 2000
-
Chapter 21. Epidemics. D. Easley and J. Kleinberg. "Networks, Crowds, and Markets: Reasoning About a Highly Connected
World".
Lecture 10:
- Chapter 17. Epidemics on networks. Mark Newman.
"Networks: An Introduction". Oxford University Press, 2010.
- Matt. J. Keeling and Ken.T.D. Eames.
Networks and Epidemics models Journal R. Soc. Interface, Vol 2, pp
295-307, 2005
-
G. Witten and G. Poulter
Simulations of infections diseases on networks
Computers in Biology and Medicine, Vol 37, No. 2, pp 195-205, 2007
-
M. Kuperman and G. Abramson
Small World Effect in an Epidemiological Model., Phys. Rev. Lett., Vol 86, No 13, pp 2909-2912, 2001
-
Manitz J, Kneib T, Schlather M, Helbing D, Brockmann D. Origin Detection During Food-borne Disease Outbreaks -
A Case Study of the 2011 EHEC/HUS Outbreak in Germany. PLoS Currents. 2014
Textbooks
Books
-
"Network Science", Albert-Laszlo Barabasi, Cambridge University Press, 2016
-
"Networks: An Introduction", Mark Newman. Oxford University Press, 2010.
-
"Social and Economic Networks", Matthew O. Jackson. Princeton
University Press, 2010.
-
"Networks, Crowds, and Markets: Reasoning About a Highly Connected
World." David Easley and John Kleinberg, Cambridge University Press 2010.
-
"Social Network Analysis. Methods and
Applications." Stanley Wasserman
and Katherine Faust, Cambridge University Press, 1994
Reviews
-
R. Albert and A-L. Barabasi.
Statistical
mechanics of complex networks.
Rev. Mod. Phys, Vol. 74, p 47-97, 2002
-
M. E. J. Newman.
The Structure and Function of
Complex Networks. SIAM Review, Vol. 45, p
167-256, 2003
-
S. Boccaletti et al.
Complex networks:
Structure and dynamics. Phys. Reports,
Vol. 424, p 175-308, 2006
-
S. N. Dorogovtsev and J. F. F. Mendes.
Evolution of
Networks.
Adv. Phys. Vol. 51, N 4, p 1079-1187
Paper collections
-
"The Structure and Dynamics of Networks". Eds.M. Newman, A.-L. Barabasi, D. Watts. Princeton University Press, 2006.
-
"Network Analysis". Eds. Ulrik Brandes, Thomas Erlebach. Lecture Notes in Computer Science. Springer, 2005
-
"Social Network Data Analysis. Ed. Charu C. Aggarwal. Springer, 2011
Software