1. Evolutionary Graph DispersionSlide 1 of 44 Background: Graph Theory Graph: G = (V,E) –V: set of vertices|V| = n –E: set of edges|E| = m Vertex –a point representing a network node –V = {a,b,c,d,e,f,g,h} Edge –A connection between two nodes –Can be directed or undirected –E = {ab, bc, bd, ce, cg, de, df, eh}

2. Evolutionary Graph DispersionSlide 2 of 44 Graphs Network: A collection of entities that are interconnected with links. Examples: – People that are friends – Computers that are interconnected – Web pages with a hyperlink to each other – Proteins that interact

3. Evolutionary Graph DispersionSlide 3 of 44 Graph Theory History Leonhard Euler –18 th century mathematician Bridges of Königsberg

4. Evolutionary Graph DispersionSlide 4 of 44 Types of Networks Social networks Technology networks Neural networks Biological networks

5. Evolutionary Graph DispersionSlide 5 of 44 Social Network www.rgnet.com/sna.html, 2007

6. Evolutionary Graph DispersionSlide 6 of 44 Sexual Networks James Moody and Jeff Grabmeier, American Journal of Sociology, 2005

7. Evolutionary Graph DispersionSlide 7 of 44 Collaboration Network

8. Evolutionary Graph DispersionSlide 8 of 44 Technology Network www.caida.org, 2005

9. Evolutionary Graph DispersionSlide 9 of 44 Neural Network Texture of the Nervous System of Man and the Vertebrates, by Santiago Ramón y Cajal (1905) Yale Scientific Magazine, Winter 2004

10. Evolutionary Graph DispersionSlide 10 of 44 Biological Networks University of Warwick, Mathematical and Computational Biology Group, 2006