Intro to network Science

Intro to Network ScienceChristopher Roach

19 Mar 2013

(1)

(3)

WTF?

Agenda

What is it?

Why now?

How do you use it?

Example

Complexity

Complexity

(2)

(2)

History

Math

(Sociology)

Computer Science

Network Characteristics

Degree Centrality

(i) = Cddeg(i)|N| ! 1

nodes = [...]degree = sum([is_neighbor(i, j) for j in nodes])degree_centrality = degree/(len(nodes) - 1)

Closeness Centrality

= li1

|N| ! 1!j"i

di,j

(i) = Cc1li

def distance(i, j): ...

nodes = [...]total_distance = 0for j in nodes: total_distance += distance(i, j)avg_distance = total_distance/(len(nodes) - 1)closeness_centrality = 1/avg_distance

Betweeness Centrality

(i) = (i) Cb1

!st!

st

!st

Eigenvector CentralityPageRank

geodesic (path)eccentricitydiameter

radiuscenter

peripherydensity

Example

http://govtrack.us

Demo

Community Detection

Senate Party Affiliation

Senate Communities

https://github.com/croach/pydata2013

References(1) Skitter data depicting a macroscopic snapshot of Internet connectivity, with

selected backbone ISPs (Internet Service Provider) colored separately by K. C. Claffy, Email: [email protected], http://www.caida.org/publications/papers/bydate/index.xml

(2) Running the Numbers: An American Self-Portrait by Chris Jordan, [email protected], http://chrisjordan.com

(3) Map of internet : 29 June 1999 by William R. Cheswick, [email protected], http://www.cheswick.com/ches/map/gallery/index.html