Gustavo Luz Blog

Consider the three small networks below, the adjacency matrix M, and the three dendrograms in shuffled order produced by hierarchical clustering applied to each graph's shortest-path distance matrix, where the dashed red line shows a cut that creates community partitions. Graph A 1 2 3 4 5 6 Graph B 1 2 3 4 5 6 Graph C 1 2 3 4 5 6 Dendrogram 1 1 2 3 4 5 6 Dendrogram 2 1 2 3 4 5 6 Dendrogram 3 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 0 1 1 0 0 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 ...

Consider the network below: A B C D E What is the Pearson degree correlation coefficient (r) for this network using Mark Newman's definition? A. r = 0, since the average degree of every node’s neighbors equals ⟨k⟩. B. r = -2/3, indicating the network is assortative. C. r = +2/3, indicating the network is disassortative. D. r = -1/2, indicating the network is assortative. E. None of the above. Original idea by: Gustavo P. C. P. da Luz