CS8803-NS Network Science Fall 2013 Instructor: Constantine Dovrolis [email protected]...
Transcript of CS8803-NS Network Science Fall 2013 Instructor: Constantine Dovrolis [email protected]...
CS8803-NSNetwork Science
Fall 2013
Instructor: Constantine [email protected]
http://www.cc.gatech.edu/~dovrolis/Courses/NetSci/
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.
Disclaimers
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
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 connected component in G(n,p) as p increases
• https://www.youtube.com/watch?v=mpe44sTSoF8
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
• 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
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