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Measuring the Significance of Structural Changes in Networks

AFRL NATO Workshop on Visualising Networks: Coping with Change and Uncertainty (IST-093/RWS-015). Rome, NY. Griffiss Institute. Oct 19-21, 2010. Measuring the Significance of Structural Changes in Networks. Chaomei Chen College of Information Science and Technology Drexel University

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Measuring the Significance of Structural Changes in Networks

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  1. AFRL NATO Workshop on Visualising Networks: Coping with Change and Uncertainty (IST-093/RWS-015). Rome, NY. Griffiss Institute. Oct 19-21, 2010 Measuring the Significance of Structural Changes in Networks Chaomei Chen College of Information Science and Technology Drexel University 3141 Chestnut Street, Philadelphia, PA 19104-2875, U.S.A. chaomei.chen@drexel.edu

  2. Paths of Foraging Learning from the Known Aware the Unknown

  3. Paths of Foraging Uncertainty, Risk, Impact Transient Scientific Frontiers Nanoscience 1997-2007

  4. 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.

  5. Structural Change Metrics: #1 • Given G(V, E), E with respect to E. • |E| • the number of different edges introduced by the new evidence.

  6. 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.

  7. Structural Change Metrics: #3 • modularity • decompose G(V, E) to a set of clusters, {Ck} • modularity= modularity(G’)/modularity(G).

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

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

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

  11. 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.

  12. 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.

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