Report

CS8803-NS Network Science Fall 2013 Instructor: Constantine Dovrolis [email protected] http://www.cc.gatech.edu/~dovrolis/Courses/NetSci/ Disclaimers The following slides include only the figures or videos that we use in class; they do not include detailed explanations, derivations or descriptions covered in class. Many of the following figures are copied from open sources at the Web. I do not claim any intellectual property for the following material. Outline • Network models – Why and how? • Random network models – ER or Poisson random graphs (covered last week) – Random graphs with given degree distribution – Watts-Strogatz model for small-world networks • Network models based on stochastic evolution – – – – Preferential attachment Variants of preferential attachment Preferential attachment for weighted networks Duplication-based models • Network models based on optimization – Fabrikant-Koutsoupias-Papadimitriou model • Application paper: modeling the evolution of the proteome using a duplication-based model • Discussion about network modeling Network models – Why and how? • What does it mean to create a “network model”? • What is the objective of this exercise? • How do we know that a model is “realistic”? • How do we know that a model is “useful”? • How do we compare two models that seem equally realistic? • Do we need models in our “brave new world” of big data? Outline • Network models – Why and how? • Random network models – ER or Poisson random graphs (covered last week) – Random graphs with given degree distribution – Watts-Strogatz model for small-world networks • Network models based on stochastic evolution – – – – Preferential attachment Variants of preferential attachment Preferential attachment for weighted networks Duplication-based models • Network models based on optimization – Fabrikant-Koutsoupias-Papadimitriou model • Application paper: modeling the evolution of the proteome using a duplication-based model • Discussion about network modeling Reference point-1: ER random graphs • G(n,m) and G(n,p) models (see lecture notes for derivations) Emergence of giant connected component in G(n,p) as p increases http://networkx.lanl.gov/archive/networkx-1.1/examples/drawing/giant_component.html Emergence of giant component • See lecture notes for derivation of the following Emergence of giant connected component in G(n,p) as p increases • https://www.youtube.com/watch?v=mpe 44sTSoF8 Outline • Network models – Why and how? • Random network models – ER or Poisson random graphs (covered last week) – Random graphs with given degree distribution – Watts-Strogatz model for small-world networks • Network models based on stochastic evolution – – – – Preferential attachment Variants of preferential attachment Preferential attachment for weighted networks Duplication-based models • Network models based on optimization – Fabrikant-Koutsoupias-Papadimitriou model • Application paper: modeling the evolution of the proteome using a duplication-based model • Discussion about network modeling The configuration model The configuration model http://mathinsight.org/generating_networks_desired_degree_distribution For instance, power-law degree with exponential cutoff Average path length Clustering coefficient in random networks with given degree distribution Outline • Network models – Why and how? • Random network models – ER or Poisson random graphs (covered last week) – Random graphs with given degree distribution – Watts-Strogatz model for small-world networks • Network models based on stochastic evolution – – – – Preferential attachment Variants of preferential attachment Preferential attachment for weighted networks Duplication-based models • Network models based on optimization – Fabrikant-Koutsoupias-Papadimitriou model • Application paper: modeling the evolution of the proteome using a duplication-based model • Discussion about network modeling • Deriving an expression for the APL in this model has been proven very hard • Here is a more important question: – What is the minimum value of p for which we expect to see a small-world (logarithmic) path length? – p >> 1/N Outline • Network models – Why and how? • Random network models – ER or Poisson random graphs (covered last week) – Random graphs with given degree distribution – Watts-Strogatz model for small-world networks • Network models based on stochastic evolution – – – – Preferential attachment Variants of preferential attachment Preferential attachment for weighted networks Duplication-based models • Network models based on optimization – Fabrikant-Koutsoupias-Papadimitriou model • Application paper: modeling the evolution of the proteome using a duplication-based model • Discussion about network modeling Preferential attachment http://www3.nd.edu/~networks/Linked/newfile11.htm Preferential attachment Continuous-time model of PA (see class notes for derivations) Avg path length in PA model Clustering in PA model “Statistical mechanics of complex networks” by R.Albert and A-L.Barabasi Outline • Network models – Why and how? • Random network models – ER or Poisson random graphs (covered last week) – Random graphs with given degree distribution – Watts-Strogatz model for small-world networks • Network models based on stochastic evolution – – – – Preferential attachment Variants of preferential attachment Preferential attachment for weighted networks Duplication-based models • Network models based on optimization – Fabrikant-Koutsoupias-Papadimitriou model • Application paper: modeling the evolution of the proteome using a duplication-based model • Discussion about network modeling Outline • Network models – Why and how? • Random network models – ER or Poisson random graphs (covered last week) – Random graphs with given degree distribution – Watts-Strogatz model for small-world networks • Network models based on stochastic evolution – – – – Preferential attachment Variants of preferential attachment Preferential attachment for weighted networks Duplication-based models • Network models based on optimization – Fabrikant-Koutsoupias-Papadimitriou model • Application paper: modeling the evolution of the proteome using a duplication-based model • Discussion about network modeling Outline • Network models – Why and how? • Random network models – ER or Poisson random graphs (covered last week) – Random graphs with given degree distribution – Watts-Strogatz model for small-world networks • Network models based on stochastic evolution – – – – Preferential attachment Variants of preferential attachment Preferential attachment for weighted networks Duplication-based models • Network models based on optimization – Fabrikant-Koutsoupias-Papadimitriou model • Application paper: modeling the evolution of the proteome using a duplication-based model • Discussion about network modeling Outline • Network models – Why and how? • Random network models – ER or Poisson random graphs (covered last week) – Random graphs with given degree distribution – Watts-Strogatz model for small-world networks • Network models based on stochastic evolution – – – – Preferential attachment Variants of preferential attachment Preferential attachment for weighted networks Duplication-based models • Network models based on optimization – Fabrikant-Koutsoupias-Papadimitriou model • Application paper: modeling the evolution of the proteome using a duplication-based model • Discussion about network modeling Outline • Network models – Why and how? • Random network models – ER or Poisson random graphs (covered last week) – Random graphs with given degree distribution – Watts-Strogatz model for small-world networks • Network models based on stochastic evolution – – – – Preferential attachment Variants of preferential attachment Preferential attachment for weighted networks Duplication-based models • Network models based on optimization – Fabrikant-Koutsoupias-Papadimitriou model • Application paper: modeling the evolution of the proteome using a duplication-based model • Discussion about network modeling Discussion about network models • Random? Stochastic evolution? Optimization-based? – How to choose? When does it matter? • How do we compare two models that seem equally realistic? • “All models are wrong but some are useful” – But when is a model useful?