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Lecture 9 Measures and Metrics

Lecture 9 Measures and Metrics. Structural Metrics. Degree distribution Average path length Centrality Degree, Eigenvector, Katz, Pagerank , Closeness, Betweenness Hubs and Authorities Transitivity Clustering coefficient Reciprocity Signed Edges and Structural balance Similarity

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Lecture 9 Measures and Metrics

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  1. Lecture 9 Measures and Metrics

  2. Structural Metrics • Degree distribution • Average path length • Centrality • Degree, Eigenvector, Katz, Pagerank, Closeness, Betweenness • Hubs and Authorities • Transitivity • Clustering coefficient • Reciprocity • Signed Edges and Structural balance • Similarity • Homophily and Assortativity Mixing

  3. Transitivity

  4. Structural Metrics:Clustering coefficient

  5. Local Clustering and Redundancy

  6. Reciprocity

  7. Signed Edges and Structural balance

  8. Similarity • Structural Equivalence • Cosine Similarity • Pearson Coefficient • Euclidian Distance • Regular Equivalence • Katz Similarity

  9. Homophily and AssortativeMixing • Assortativity: Tendency to be linked with nodes that are similar in some way • Humans: age, race, nationality, language, income, education level, etc. • Citations: similar fields than others • Web-pages: Language • Disassortativity: Tendency to be linked with nodes that are different in some way • Network providers: End users vs other providers • Assortative mixing can be based on • Enumerative characteristic • Scalar characteristic

  10. Modularity (enumerative) • Extend to which a node is connected to a like in network • + if there are more edges between nodes of the same type than expected value • - otherwise is 1 if ciand cj are of same type, and 0 otherwise err is fraction of edges that join same type of vertices ar is fraction of ends of edges attached to vertices type r

  11. Assortativecoefficient (enumerative) • Modularity is almost always less than 1, hence we can normalize it with the Qmax value

  12. Assortativecoefficient (scalar) • r=1, perfectly assortative • r=-1, perfectly disassortative • r=0, non-assortative • Usually node degree is used as scale

  13. Assortativity CoefficientVarious Networks M.E.J. Newman. Assortative mixing in networks

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