Lecture 9 Measures and Metrics
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Transcript of Lecture 9 Measures and Metrics
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Lecture 9
Measures and Metrics
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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
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Transitivity
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Structural Metrics:Clustering coefficient
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Local Clustering and Redundancy
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Reciprocity
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Signed Edges and Structural balance
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Similarity
Structural Equivalence Cosine Similarity
Pearson Coefficient
Euclidian Distance
Regular Equivalence Katz Similarity
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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
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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 ci and 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
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Assortative coefficient (enumerative) Modularity is almost always less than 1, hence we can
normalize it with the Qmax value
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Assortative coefficient (scalar)
r=1, perfectly assortative r=-1, perfectly disassortative r=0, non-assortative
Usually node degree is used as scale
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Assortativity Coefficient Various Networks
13M.E.J. Newman. Assortative mixing in networks