Measuring the Significance of Structural Changes in Networks

Chaomei ChenCollege of Information Science and Technology

Drexel University3141 Chestnut Street, Philadelphia, PA 19104-2875, U.S.A.

chaomei.chen@drexel.edu

AFRL NATO Workshop on Visualising Networks: Coping with Change and Uncertainty (IST-093/RWS-015). Rome, NY. Griffiss Institute. Oct 19-21, 2010

Paths of ForagingLearning from the Known Aware the Unknown

Nanoscience 1997-2007

Paths of ForagingUncertainty, Risk, Impact

Transient Scientific Frontiers

Outline• Motivation

– How ideas in a newly published scientific paper may revolutionize the current knowledge structure of a field

– How the increase of gas price may change the traffic load on a public transportation network

– How a new discovery may alter the structure of a network of proteins– How a new science and technology policy may change a network of collaborating

universities and companies• Questions

– Will newly available information change the current structure of the network?– If so, to what extent?

• Our Solution– Introduce a set of information metrics to measure the degree of structural change

induced by newly available information at the system level.• Benefits

– Identify the source of information that would produce the most profound impact on the structure of an existing network.

– Compare sources that appear to provide conflicting information.

Structural Change Metrics: #1

• Given G(V, E), E with respect to E. • |E|– the number of different edges introduced by the

new evidence.

Structural Change Metrics: #2

• centrality

– The node centrality of a network G(V, E), C(G), is a distribution of the centrality scores of all the nodes, <c1, c2, …, cn>, where ci is the centrality of node ni, and n is |V|, the total number of nodes. The degree of structural change E can be defined in terms of the K-L divergence.

Structural Change Metrics: #3

• modularity

– decompose G(V, E) to a set of clusters, {Ck}– modularity= modularity(G’)/modularity(G).

1-year slices citers criteria space nodes links networks size modularity

2006 1 top 200 19 19 171 G2006 1919 0.0000

2007 17 top 200 338 200 2634 G2007 216216 0.7340

2008 16 top 200 1526 200 9261 G2008 399399 0.2268

2009 31 top 200 868 200 2432 G2009 558558 0.3269

2010 11 top 200 475 200 2933

Table 1: The accumulative networks prior to the streaming articles.

Q C TC NR Author Year Title Source4.5329 .0567 18 610 JUDIT BARILAN 2008 Informetrics at the beginning of the 21st century - A review

J INFORMETR

2.0735 .0236 3 370 STEVEN A. MORRIS 2008 Mapping research specialties

ANNU REV INFORM SCI TECH

1.5902 .0044 3 106 CHAOMEI CHEN 2009 Towards an explanatory and computational theory of scientific discovery

J INFORMETR

.8241 .0024 1 62 ERJIA YAN 2009 Applying Centrality Measures to Impact Analysis: A Coauthorship Network Analysis

J AM SOC INF SCI TECHNOL

.7701 .0014 2 29 YOSHIYUKI TAKEDA 2009 Optics: a bibliometric approach to detect emerging research domains and intellectual bases

SCIENTOMETRICS

.7079 .0037 1 84 KATY BORNER 2009 Visual conceptualizations and models of science

J INFORMETR

.4769 .0003 0 23 YOSHIYUKI TAKEDA 2010 Tracking modularity in citation networks

SCIENTOMETRICS

.4635 .0026 1 45 YOSHIYUKI TAKEDA 2009 Nanobiotechnology as an emerging research domain from nanotechnology: A bibliometric approach

SCIENTOMETRICS

.4124 .0008 0 42 ALEKS ARIS 2009 Visual Overviews for Discovering Key Papers and Influences Across Research Fronts

J AM SOC INF SCI TECHNOL

.3574 .0012 0 33 ERJIA YAN 2009 The Use of Centrality Measures in Scientific Evaluation: A Coauthorship Network Analysis

PROC INTER CONF SCI INFOMET

.3408 .0006 1 37 NEES JAN VAN ECK 2010 Software survey: VOSviewer a computer program for bibliometric mapping

SCIENTOMETRICS

.3302 .0005 0 19 CHAOMEI CHEN 2009 Visual Analysis of Scientific Discoveries and Knowledge Diffusion

PROC INTER CONF SCI INFOMET

.3016 .0025 6 76 DIANA LUCIOARIAS 2009 The dynamics of exchanges and references among scientific texts and the autopoiesis of discursive knowledge

J INFORMETR

.2350 .0007 0 20 DEMING LIN 2009 Statistical Characteristics of an Evolving Co-citation Network: The Distribution of Betweenness Centrality

PROC INTER CONF SCI INFOMET

.2253 .0014 0 64 KATARINA LARSEN 2009 Co-authorship Networks in Development of Solar Cell Technology: International and Regional Knowledge Interaction

ADV SPAT SCI

.2138 .0001 0 35 JIAN ZHANG 2009 Visualizing the Intellectual Structure with Paper-Reference Matrices

IEEE TRANS VISUAL COMPUT GR

.1808 .0027 0 10 TSUNG TENG CHEN 2009 Visualizing Contextual Information of Cocitation Networks

INFORMATION VISUALIZATION

.1576 .0001 0 37 OLLE PERSSON 2010 Identifying research themes with weighted direct citation links

J INFORMETR

.1552 .0004 0 37 L. Y. TANAKA 2009 Sequential result refinement for searching the biomedical literature

J BIOMED INFORM

Table 2: Papers ranked by the modularity change rate Q, i.e. modularity.

Dependent Variable: CitationsSource

Type III Sum of Squares df Mean Square F Sig.

Partial Eta Squared

Corrected Model 112675.351a 4 28168.838 58.578 .000 .890

Intercept 2331.753 1 2331.753 4.849 .036 .143

Modularity 801.177 1 801.177 1.666 .207 .054

Centrality 4098.399 1 4098.399 8.523 .007 .227

alpha 46.711 1 46.711 .097 .758 .003

beta 1263.181 1 1263.181 2.627 .116 .083

Error 13945.494 29 480.879

Total 214646.000 34

Corrected Total 126620.845 33

a. R Squared = .890 (Adjusted R Squared = .875)

b. Weighted Least Squares Regression - Weighted by NR

Table 3: The Tests of Between-Subjects Effects b. Data source: 76 papers that cited [3].

Table 4: Parameter Estimates a

Dependent Variable: CitationsParameter

B Std. Error t Sig.

95% Confidence Interval Partial Eta SquaredLower Bound Upper Bound

Intercept 1.541 .700 2.202 .036 .110 2.971 .143 Modularity 4.861 3.766 1.291 .207 -2.841 12.564 .054

Centrality 594.105 203.504 2.919 .007 177.891 1010.318 .227

alpha .011 .035 .312 .758 -.061 .083 .003beta -.210 .130 -1.621 .116 -.476 .055 .083a. Weighted Least Squares Regression - Weighted by NR

Conclusion

• A lot of more work needs to be done. • Metrics of structural variation are promising

measures for detecting potential sources of change in the structure of a network.

• Such metrics provide evidence provenance for decision making.

• We expect that these metrics can provide valuable information needed in the analysis of the dynamics of networks and dealing with changes and uncertainties.

ACKNOWLEDGEMENTS

• The work is in part supported by the NSF under the grant # IIS-0612129. The author wishes to thank Thomson Reuters for providing an extensive access to the Web of Science.