1. STRUCTURAL SIMILARITIES OF COMPLEX NETWORKS: A COMPUTATIONAL MODEL BY EXAMPLE OF WIKI GRAPHS For CS790 Complex Network A Paper Presented by Bingdong Li 11/18/2009

2. Credit Mehler, Alexander(2008) 'STRUCTURAL SIMILARITIES OF COMPLEX NETWORKS: A COMPUTATIONAL MODEL BY EXAMPLE OF WIKI GRAPHS',Applied Artificial Intelligence,22:7,619 — 683

3. Outline Objectives Introduction Wiki Graphs Quantitative Network Analysis Classification Examples Conclusion

4. Objectives Looking for a framework for representing and classifying large complex networks Focus on networks as a whole unit to be classified

5. Outline Objectives Introduction Wiki Graphs Quantitative Network Analysis Classification Examples Conclusion

6. Introduction Through wiki graph considering its size, structure and complexity

7. Introduction Agent(A), document(B), and word network(C)

8. Introduction Network A, vertices denote agents whose collaborations span the edges. Network B, vertices denote pages whose hyperlinks span the edges of the graph. Network C, vertices denote words whose lexical associations

9. Introduction Hypotheses about the tripartite networks – Network correlation hypothesis(NCH): agent, document, and word networks correlate with respect to their small world property – Network separability Hypothesis(NSH): social and linguistic networks can be reliably separated by means of their topological characteristics

10. Introduction Problems to solve – How to reliably segment and classify networks in order to map their constituents and similarity distributions – A efficient data structure for representing networks

11. Introduction Building blocks – A graph model expressive enough to map multilevel networks – A computational model of the similarities of instance of this graph model together with a classification algorithm in terms of Quantitative Network Analysis (QNA) – A model of the distribution of the kind of networking manifested by wikis

12. Introduction Overall approach – Investigate the separability of various topological features – Distinguish less informative from more informative topological characteristics

13. Outline Objectives Introduction Wiki Graphs Quantitative Network Analysis Classification Examples Conclusion

14. Wiki Graphs Construct the Wiki graphs – Agent, document and linguistic – Three reference points Micro-level, page-internal structure meso-level, correspond to websites as thematically and functionally closed units of web-based communication macro-level, topology of the corresponding wiki document network as a whole

15. Wiki Graphs

16. New concepts – Generalized Tree(GT) – Labeled Typed Generalized Tree – Typed Graph(TG) – K-Partite Type Graph – Hypergraph – Realization of a Hypergraph – Directed graph induced by a directed hypergraph

17. Wiki Graphs

18. A typed hypergraph as a model of a wiki document network (a) and its realization(b)

19. Wiki Graphs A multilevel graph stratified into three component graphs (edges between vertices of different component graphs are denoted by dashed lines)

20. Outline Objectives Introduction Wiki Graphs Quantitative Network Analysis Classification Examples Conclusion

21. Quantitative Network Analysis Follows Quantitative Structure Analysis(QSA) – Segment the constituents of the target objects – Feature selection and validation – Feature aggregation and target object representation

22. Quantitative Network Analysis Mapping two input networks onto vectors of composite features as a prerequisite of validating their similiarity

23. Quantitative Network Analysis

24. Algorithm 1. for all F’ ε 2 F do 2. for X[F’] Λ Y[F’] do 3. for all CMj ε {ClusteringMethodm|m ε M} do 4. for all Sk ε SetOfParameterSettings(CMj) do 5. ComputeF-MeasureValue(Z[F’],CMj,Sk),Z ε {X,Y} 6. end for 7. end for 8. end for 9. end for

25. Outline Objectives Introduction Wiki Graphs Quantitative Network Analysis Classification Examples Conclusion

26. Classification Example – Wiki Corpus Ontological separability

27. Classification Example – Wiki Corpus Functional separability

28. Outline Objectives Introduction Wiki Graphs Quantitative Network Analysis Classification Examples Conclusion

29. Presented a formal framework for representing, analyzing, and classifying complex networks on variant levels (here, linguistic networks on agent, document and lexico-grammatical units)

30. Conclusion The correlation of small world topologies on the level of social and textual network The distinguishability of ontologically and functionally divergent networks An approach to structure-oriented machine learning in the area of large complex networks

31. Discussion