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

  1. Statistical properties and modeling of networks
  2. Network structure and dynamics
  3. Processes on networks
  4. Predictions on networks (ML)
  5. Network embeddings (DL)
  6. Graph neural networks (DL)

Seminars/Labs

Youtube channel with lectures 2021

Module 3

Lectures

  1. [10.01.2022] Introduction to network science. [Lecture 1]
    Introduction to the complex network theory. Network properties and metrics.
  2. [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.
  3. [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
  4. [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.
  5. [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.
  6. [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.
  7. [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
  8. [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.
  9. [14.03.2022] Mathematical modeling of epidemics [Lecture 9]
    Compartamental epidemic models: SI, SIS, SIR. Limiting cases. Basic reproduction number.
  10. [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

  1. [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.
  2. [11.04.2020] Machine learning on graphs. Node classification [Lecture 12]
    Node labeling. Label propagation. Iterative classification. Semi-supervised learning. Regularization on graphs
  3. [18.04.2020] Link prediction [Lecture 13]
    Link prediction problem. Proximity measures. Scoring algorithms. Prediction by supervised learning. Performance evaluation.
  4. Additional reading material

    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

    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