Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

    címtáras azonosítással

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    Structure and Dynamics of Complex Networks

    A tantárgy neve magyarul / Name of the subject in Hungarian: Komplex hálózatok struktúrája és dinamikája

    Last updated: 2010. november 11.

    Budapest University of Technology and Economics
    Faculty of Electrical Engineering and Informatics

    Mérnök informatikus szak

    BSc képzés

    Course ID Semester Assessment Credit Tantárgyfélév
    VISZA093   3/1/0/v 4  
    3. Course coordinator and department Dr. Recski András,
    Web page of the course
    4. Instructors






    János KERTÉSZ




    Department of Theoretical Physics


    Péter CSERMELY




    Department od Medical Chemistry, Molecular Biology and Pathobiochemistry, Semmelweis University


    7. Objectives, learning outcomes and obtained knowledge

    Complex systems consist of many interacting units and are characterized by nonlinearity, positive and negative feedback, and emergent cooperative phenomena. Examples are the brain, the cell, the internet, the economy etc. Recent developments in network science provide efficient tools to handle such systems. In the first part of the lectures we will present the basics of complex network theory, including small world and scale free properties, important measures, spreading and breakdown phenomena, weighted and directed graphs. In the second part examples will be analyzed from information technology, economy, sociology and biology.

    8. Synopsis
    1. Introduction


    Complex systems


    Hierarchical structures


    Elements of percolation theory, critical phenomena, scaling




    1. Networks, basic concepts of graph theory


    Properties of real networks: small-worldness, scale freeness, community structure, hierarchies


    Centrality measures


    Clustering, assortativity




    Characteristics of weighted networks


    Correlation networks



    1. Models


    Erdős Rényi








    Fitness-models, rich-gets-richer, Bose-Einstein condensation




    1. Community detection


    Modularity based methods


    Local methods


    Overlapping communities


    Hierarchical clustering in weighted graphs





    1. Stability of networks


    Error tolerance and vulnerability


    Spreading phenomena, diseases, models, vaccination


    Breakdown in a fuse network – the Big Blackout



    1. Random walks on networks


    Diffusion and Laplace operator


    Transport phenomena



    1. The Internet as a complex network 


    Statistical properties of the WWW


    Wikipedia: The complex network of cooperative value creation



    1. Social networks


    Data collection, traditional and new (ICT-based) forms


    Graphs representing social networks: binary, signed, weighted


    The importance of weak ties


    Email and mobile phone networks and what we can learn from them



    1. Complex networks in economy and finance


    Networks of companies


    Networks of banks: The domino effect


    Correlation networks and portfolio optimization



    1. Cellular networks


    Protein structures: localization of active centers, landscape of conformational changes, evolution


    Protein-protein interaction networks: hub and module dynamics in cellular changes


    Signaling and gene regulatory networks



    1. Networks of neurons and ecosystems


    Network construction from emergent behavior (reverse engineering) and from correlations


    Changes in brain default networks during aging and disease


    Ecological networks: keystone species and prediction of ecosystem damage



    1. Networks and drug design


    Human disease and drug-target networks


    Determination of drug binding sites in amino acid networks


    Prediction of novel drug targets by network analysis


    9. Method of instruction Lectures, recitations, project-based computer assignments


    10. Assessment The students are requested to participate actively in the exercises, where they can acquire up-to-date knowledge on the subject at the skill level. Exercises will be adjusted to the lectures and the students will get home work, which they have to solve in some cases individually, in other cases in team. The tasks include analytical problem solving, programming, data search, library/internet survey.



    The grade is based on the exercises (60 %) and on a final test (40 %).


    12. Consultations You can reach the instructors at the following e-mail address for consultation:


    János KERTÉSZ:


    Péter CSERMELY:


    13. References, textbooks and resources A.L. Barabási: Linked (Perseus, 2002);


    R. Albert and A.L. Barabási: Statistical Mechanics of Complex Networks, Rev. Mod. Phys. 74, 47-97 (2002); M.E.J. Newman, The structure and function  of complex networks, SIAM Review, 45, 167-256 (2003);


    S.N. Dorogovtsev and J.F.F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW, Oxford University Press (2003);


    R. Pastor-Satorras, A. Vespignani, Evolution and Structure of the Internet: A Statistical Physics Approach, Cambridge (2004);


    M. O. Jackson: Social and Economic Networks, Princeton Univ. Press (2008);


    P. Csermely: Weak Links: The Universal Key to the Stability of Networks and Complex Systems, Springer (2009).


    14. Required learning hours and assignment
    Number of contact hours




    Preparation to the classes




    Preparation to the tests







    Assigned reading



    Preparation to the exam








    15. Syllabus prepared by






    János KERTÉSZ




    Department of Theoretical Physics


    Péter CSERMELY




    Department od Medical Chemistry, Molecular Biology and Pathobiochemistry, Semmelweis University