Matching networks, matrices, and dendrograms

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 1 0 1 1 0 0 0 1 0 1 0 0 0 1 1 0

Decide whether each of the three statements below is True or False:

I. The adjacency matrix M was computed on Graph A.

II. Dendrogram 1 corresponds to Graph C.

III. Dendrogram 2 corresponds to Graph A.

Which option correctly gives the truth values of statements I, II, III?

A. T — T — T

B. T — T — F

C. T — F — T

D. F — T — F

E. None of the above.

Original idea by: Gustavo P. C. P. da Luz

Comments

  1. Joao MeidanisMay 23, 2026 at 11:35 AM

    Nice question, but I see some problems. The dendrograms have nodes with 3 or 4 children. Usually we have just 2 children. Also, adding adjacency matrices here does not contribute to a better question. I prefer to pass on it.

    ReplyDelete

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