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 Homophily and Assortativity Mixing 2

Transitivity 3

Structural Metrics: Clustering coefficient 4

Local Clustering and Redundancy 5

Reciprocity 6

Signed Edges and Structural balance 7

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

Homophily and Assortative Mixing 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 9

Modularity (enumerative) 10

Assortative coefficient (enumerative) 11

Assortative coefficient (scalar) 12

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