COMS 6998-06 Network TheoryWeek 11

Dragomir R. RadevWednesdays, 6:10-8 PM

325 Pupin TerraceFall 2010

(29) Bibliometrics

Early work

• The Science Citation Index (1960)– More than 8,700 journals in the natural and

social sciences

• Eugene Garfield

• de Solla Price – study of networks of papers and citation patterns

Recent systems

• Citeseer

• Rexa

• Google Scholar

• ACL Anthology Network

Garfield’s indices

• Journal citation reports• Impact factor:

– Computed over a three-year period as B/A, where• First two years: A = number of citable items• Third year: B = the number of citations to them

• In science (2006)– Science (30.03)– Nature (26.68)– PNAS (9.64)

Criticism

• Favor certain fields and types of research

• Absolute value is meaningless

• Ignores certain type of scholarly work (e.g., books, software, conference papers)

• Possible to manipulate

• Self-citations

• Ignore citation type (this applies to all other metrics!)

Citation types

[Weinstock 1971]

Networks of scientific papers (1965)

• In a given year, about 35% of the papers of all existing papers are not cited at all. Another 49% are cited only once. The rest are cited an average of 3.2 times each.

• Degree coefficient is about 2.5-3.0

• 7% annual growth

• Most papers are obsolete after 10 years

De Solla Price 1965

Miscellaneous metrics

• Citation count• Impact factor• Pagerank (e.g., http://www.eigenfactor.org/)• H-index

H-index

• Proposed by Jorrge Hirsch of UCSD in 2005

• Equals the number of papers of yours, h that have been cited at least h times.

• For physicists, 12=tenure, 18=full prof, 45=NAS (statement by Hirsch)

• See demo (ACL Anthology Network)

• also: PoP (guess what it means?)

cita

tio

ns

papers

h

Criticism

• Galois’s is 2 (short career)

• Hard to compare two people with the same score but very different distribution

• Hugely different based on the underlying database

ExampleAAN Google Scholar Name

16 38 Ken Church

15 32 Kevin Knight

14 30 Ralph Grishman

14 33 Aravind Joshi

14 45 Hermann Ney

14 45 Fernando Pereira

13 30 David Yarowsky

12 24 Michael Collins

12 32 Chris Manning

12 32 Daniel Marcu

12 39 Kathy McKeown

12 35 Robert Mercer

12 25 Franz Och

12 25 Yves Schabes

12 34 Stuart Shieber

11 23 Eric Brill

11 37 Eugene Charniak

11 24 Ido Dagan

11 25 Mark Johnson

11 30 Philip Resnik

88 Hector Garcia-Molina (Stanford), ACM Fellow, Member of the National Academy of Engineering 81 Jeffrey D. Ullman (Stanford), ACM Fellow, Member of the National Academy of Engineering76 Robert Tarjan (Princeton), Turing Award, ACM Fellow, Member of the National Academy of Engineering 75 Deborah Estrin (UCLA), ACM Fellow, IEEE Fellow 75 Don Towsley (U Mass, Amherst), ACM Fellow, IEEE Fellow 73 Ian Foster (Argonne National Laboratory & U Chicago) 71 Scott Shenker (Berkeley), ACM Fellow, IEEE Fellow 70 David Culler (Berkeley), ACM Fellow, Member of the National Academy of Engineering 68 Takeo Kanade (CMU), ACM Fellow, IEEE Fellow, Member of the National Academy of Engineering 61 Mario Gerla (UCLA), IEEE Fellow 61 Nick Jennings (U Southampton), Fellow of the Royal Academy of Engineering 58 Anil K. Jain (Michigan State U), ACM Fellow, IEEE Fellow 57 Demetri Terzopoulos (UCLA), ACM Fellow, IEEE Fellow, Member of the European Academy of Sciences 56 Randy H. Katz (Berkeley), ACM Fellow, IEEE Fellow, Member of the National Academy of Engineering 56 Steven Salzberg (U Maryland) 55 Jennifer Widom (Stanford), ACM Fellow, Member of the National Academy of Engineering 54 Jack Dongarra (U Tennessee), ACM Fellow, IEEE Fellow, Member of the National Academy of Engineering54 David E. Goldberg (UIUC) 54 Ken Kennedy (Rice), ACM Fellow, IEEE Fellow, Member of the National Academy of Engineering 54 Amir Pnueli (Weizmann and New York University), Turing Award, ACM Fellow, Member of the National Academy of Engineering 54 Herbert A. Simon (CMU), Turing Award, ACM Fellow, Nobel Laureate 53 Sally Floyd (ICSI), ACM Fellow 53 Tomaso Poggio (MIT) 53 Eduardo Sontag (Rutgers), IEEE Fellow 52 Rakesh Agrawal (Microsoft), ACM Fellow, IEEE Fellow, Member of the National Academy of Engineering 52 Stanley Osher (UCLA), Member of the National Academy of Sciences 52 Christos H. Papadimitriou (Berkeley), ACM Fellow, Member of the National Academy of Engineering 51 Jiawei Han (UIUC), ACM Fellow 51 Richard Karp (Berkeley), Turing Award, ACM Fellow, Member of the National Academy of Engineering 51 Alex Pentland (MIT)

[using PoP; collected by Jens Palsberg (UCLA)]http://www.cs.ucla.edu/~palsberg/h-number.html

Recent study (An et al. 2004)

• 31.5% of the papers have been cited.• In-degree power law coefficient 1.71• Diameters:

– Neural networks (n=23,371) d=24, ud=18– Automata (n=28,168) d=33, ud=19– Software eng (n=19,018) d=22, ud=16

• Largest connected components:– NN WCC=79.6%– Automata WCC=92%– SE WCC=87.9%

Collaboration networks

[Beaver 2001; Glaenzel 2003]

Many reasons why people collaborate:

[Paul Erdos]

(23) The Ising model

(24) Percolation on graphs

What is percolation [Grimmett 1999]

• Will water flow through a porous stone?

• Let p be the probability that an edge is open.• This process is called “bond percolation”• Paths (percolation) appear at p=0.5059. This is

a quintessential example for phase transitions

p

q(p)

1

1

(1,1)

• Example: ferromagnetism. The Curie point is when there is no longer spontaneous magnetization

• Generic example of a magnetic field:

[http://ibiblio.org/e-notes/Perc/ising.htm]

The Ising model

• Given a lattice in D-dimensional space.

• Each vertex can be -1 or 1.

• Configurations: specific assignments of -1 and 1

• The energy of a configuration is

• In statistical physics: P(S) ~ e-βE

[http://ibiblio.org/e-notes/Perc/trans.htm]

Demo

• http://webphysics.davidson.edu/applets/ising/default.html

• http://stp.clarku.edu/simulations/ising/ising2d.html

• http://www.phy.syr.edu/courses/ijmp_c/Ising.html • Ferromagnetic alignment (J>0)• Temperature tends to break the alignment:

causes the spins to randomly change their values

• External magnetic field tends to support the alignment

Site percolation• The critical value is around 0.59 but has

not been derived analytically.

Demo

• http://theorie.physik.uni-wuerzburg.de/~reents/ComputationalPhysics/percgr.html

• http://ibiblio.org/e-notes/Perc/perc.htm

• http://ibiblio.org/e-notes/Perc/distr.htm

• http://stp.clarku.edu/simulations/

(15) Diffusion on graphs

Epidemics in small worlds• Epidemic = in the limit of a large graph, a non-

zero fraction is infected.• Fully mixed networks – everyone is connected to

everyone the same way.• In real life this is not true.• Let f = average number of shortcuts per vertex.• Let k = 1: every vertex is connected to at least

its one nearest neighbor.• For large L (#vertices), the prob. that two

random vertices have a shortcut is:

2

2 21 1

kfLkf

L L

Moore and Newman 2000. Epidemics and Percolation in small-world networks.

Moore and Newman 2000 cont’d

Moore and Newman 2000 cont’d

More recent work

• Newman 2002– Outbreak size distribution– Degree of infected individuals– Bipartite graphs