STRUCTURAL SIMILARITIES OF COMPLEX NETWORKS: A COMPUTATIONAL MODEL BY EXAMPLE OF WIKI GRAPHS

For CS790 Complex NetworkA Paper Presented by Bingdong Li

11/18/2009

Credit

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

Outline

• Objectives• Introduction• Wiki Graphs• Quantitative Network Analysis• Classification Examples• Conclusion

Objectives

• Looking for a framework for representing and classifying large complex networks

• Focus on networks as a whole unit to be classified

Outline

• Objectives• Introduction• Wiki Graphs• Quantitative Network Analysis• Classification Examples• Conclusion

Introduction

• Through wiki graph considering its size, structure and complexity

Introduction

• Agent(A), document(B), and word network(C)

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

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

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

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

Introduction

• Overall approach– Investigate the separability of various topological

features– Distinguish less informative from more informative

topological characteristics

Outline

• Objectives• Introduction• Wiki Graphs• Quantitative Network Analysis• Classification Examples• Conclusion

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

Wiki Graphs

Wiki Graphs

• 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

Wiki Graphs

Wiki Graphs

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

Wiki Graphs

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

Outline

• Objectives• Introduction• Wiki Graphs• Quantitative Network Analysis• Classification Examples• Conclusion

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

Quantitative Network Analysis

• Mapping two input networks onto vectors of composite features as a prerequisite of validating their similiarity

Quantitative Network Analysis

Quantitative Network Analysis

• Algorithm1. for all F’ ε 2F do2. for X[F’] Λ Y[F’] do3. for all CMj ε {ClusteringMethodm|m ε M} do4. for all Sk ε SetOfParameterSettings(CMj) do5. ComputeF-MeasureValue(Z[F’],CMj,Sk),Z ε {X,Y}6. end for7. end for8. end for9. end for

Outline

• Objectives• Introduction• Wiki Graphs• Quantitative Network Analysis• Classification Examples• Conclusion

Classification Example – Wiki Corpus

• Ontological separability

Classification Example – Wiki Corpus

• Functional separability

Outline

• Objectives• Introduction• Wiki Graphs• Quantitative Network Analysis• Classification Examples• Conclusion

Conclusion

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

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

Discussion