small world graphs
Download
Skip this Video
Download Presentation
Small World Graphs

Loading in 2 Seconds...

play fullscreen
1 / 15

Small World Graphs - PowerPoint PPT Presentation


  • 110 Views
  • Uploaded on

Small World Graphs. Amber Rice. Defining a Small World Graph. Relatively HIGH Clustering Coefficient Relatively LOW Characteristic Path Length. Clustering Coefficient. Measure of degree to which vertices in a graph tend to cluster together

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Small World Graphs' - cayla


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
defining a small world graph
Defining a Small World Graph
  • Relatively HIGH Clustering Coefficient
  • Relatively LOW Characteristic Path Length
clustering coefficient
Clustering Coefficient
  • Measure of degree to which vertices in a graph tend to cluster together
  • If A is connected to B and B is connected to C, then there’s a heightened probability that A is connected to C.
clustering coefficient1
Clustering Coefficient
  • C =
  • Where:
  • “triangles” are K graphs
  • “connected triples” are nonisomorphic paths of length two

3

finding clustering coefficient
Finding Clustering Coefficient

One Triangle

8 Connected Triples

So the Clustering Coefficient is 3/8.

characteristic path length
Characteristic Path Length
  • The average number of “steps” along the shortest paths for all possible pairs of vertices in the graph
  • The median of the means of shortest distances between all pairs of vertices
finding characteristic path length
Finding Characteristic Path Length

First, find the distances between all the vertices and each average length.

A – 1, 1, 2, 2 mean(A) = 6/4

B – 1, 1, 2, 2 mean(B) = 6/4

C – 1, 1, 1, 1 mean(C) = 4/4

D – 1, 2, 2, 2 mean(D) = 7/4

E – 1, 2, 2, 2 mean(E) = 7/4

Next, take the median of the averages.

Median ( 4/4, 6/4, 6/4, 7/4, 7/4 ) = 6/4

A

D

C

E

B

So, the Characteristic Path Length of this graph is 6/4.

conclusions
Conclusions
  • New topic
    • Not much information
  • Likely to be very important in the future
  • My honors project
    • Social networks on campus
references

References

Newman, M. E. J. (2003). The structure and function of complex networks. SIAM Review, 45(2):167-256.

http://www.cmth.bnl.gov/~maslov/citerank/images/CitationNetworkDiagram1.gif

http://www.bordalierinstitute.com/images/worldwideweb.jpeg

http://images.google.com/imgres?imgurl=http://cmore.soest.hawaii.edu/cruises/operex/images/terrestrial_food_web

http://onlineaikido.com/blog_resources/pictures/neural_network_3.jpg

http://www.technologyreview.com/articlefiles/fairley80701.jpg

http://www.barnabu.co.uk/wp-content/uploads/usa-air-routes-google-earth.JPG

slide15
http://polymer.bu.edu/~amaral/Sex_partners/idahlia_web.jpg

http://film-buff.tripod.com/kevinbacon.jpg

http://insanityoverrated.files.wordpress.com/2009/02/six-degrees1.jpg

http://en.wikipedia.org/wiki/Small_world_experiment

http://en.wikipedia.org/wiki/Small-world_network

http://en.wikipedia.org/wiki/Clustering_coefficient

http://getoutfoxed.com/files/small-world-ring-with-rando.png

http://www.amazon.com/Small-Worlds-Duncan-J-Watts/dp/0691005419

ad