xiaofan wang [email protected] 2014 network science: an introduction

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  • Slide 1
  • Xiaofan Wang [email protected] 2014 Network Science: An Introduction
  • Slide 2
  • Slide 3
  • Network Science Measuring Data Measuring Data Discovering Property Modeling Network Modeling Network Analysis Behavior Analysis Behavior Design Performance
  • Slide 4
  • Collect enough information so that you can Describe (correctly) Quantify (properly) Formulate (mathematically ) Predict (reasonably) Control (powerfully)
  • Slide 5
  • Communication Transportation Power Grid Social Economical NetworkSpreading Biological
  • Slide 6
  • Virus Fasion Behavior Rumor Belief Spreading on Social Networks (video) Spreading on Social Networks (video) Opinion
  • Slide 7
  • Theoretical Science Graph Theory Game Theory Statistical Physics Computer Science Applied Science Communication Science Power Engineering Life Science Social Science
  • Slide 8
  • For every technology, the first ten years is the development, and the second ten years is when the market follows.
  • Slide 9
  • Science, in general, is a lot better at breaking complex things into tiny parts than it is at figuring out how tiny parts turn into complex things.
  • Slide 10
  • Interdisciplinary nature Data-driven nature Quantitative nature Computational nature
  • Slide 11
  • Interdisciplinary nature Data-driven nature Quantitative nature Computational nature
  • Slide 12
  • Graph Theory Spectral Graph Theory Markov Chain Theory Fan Chung UCSD
  • Slide 13
  • A.-L. Barabsi Northeastern Mark Newman Michigan Mean-Field Theory Phase Transition Percolation Theory
  • Slide 14
  • Jon Kleinberg Cornell
  • Slide 15
  • Liu Y Y, Slotine J J, Barabsi A L. Nature, 2011, 473(7346): 167-173.
  • Slide 16
  • Sinan Aral MIT
  • Slide 17
  • Lev Muchnik, Sinan Aral, and Sean J. Taylor, Social Influence Bias: A Randomized Experiment, Science 9 August 2013: 341 (6146), 647-651. 101281 32%
  • Slide 18
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  • Slide 21
  • Unweighted Undirected Weighted Undirected Unweighted Directed Weighted Directed
  • Slide 22
  • 101 144 101 242
  • Slide 23
  • Slide 24
  • No Multi-edge No Self-edge
  • Slide 25
  • Slide 26
  • 99.9% 32% Facebook Friendship network: Facebook Love network:
  • Slide 27
  • Many networks have a unique giant component
  • Slide 28
  • If you have 2 large-components each occupying roughly 1/2 of the graph. How many random edges do you need to add so that the probability that the two components join into one giant component is greater than 0.9? (a) 1-5 edge additions (b) 6-10 edge additions (c) 11-15 edge additions (d) 16-20 edge additions
  • Slide 29
  • (Giant weakly connected component, GWCC) Bow-tie structure (SCC) (IN) (OUT) (TENDRILS)
  • Slide 30
  • (Giant weakly connected component, GWCC) Bow-tie structure (SCC) (IN) (OUT) (TENDRILS)
  • Slide 31
  • Average degree
  • Slide 32
  • Out-Degree In-Degree
  • Slide 33
  • Whole net out-degree equals to in-degree Single node out-degree may not equal to in-degree
  • Slide 34
  • = 349 54785
  • Slide 35
  • Globally coupled net k=N-1, M~O(N 2 ) Practical net