Degree correlation

 Observe the following heatmaps which represent the correlation matrices eij of two different networks (1) and (2). The bars represent the probability of connection between nodes with degrees k1 and k2.

Notice that some areas are highlighted in the figures, i.e. (u), (v), (w), and (x).

Analyze the following statements regarding those areas and network characteristics to further mark them as True or False:

1) In network (1), the highlighted area (u) refers to the connection between a hub and a low-degree node, while the area (v) refers to the connection between two hubs.

2) In network (2), the highlighted area (w) refers to the connection between two low-degree nodes, while the area (x) refers to the connection between two hubs.

3) Network (1) represents a disassortative network since the probability of connection is stronger in the secondary diagonal.

4) Network (2) represents an assortative network. Also, if we applied degree-preserving randomization to it knnR−S(k), and it matched the original function knn(k), then the observed correlations could be attributed to structural constraints imposed by the degree distribution.

Chose the correct alternative:

A) T-T-F-F

B) F-T-T-T

C) F-T-T-F

D) T-T-T-F

E) None of the above

 

Original idea by Gabriela Caspa

Comentários

  1. Joao Meidanis10 de maio de 2026 às 13:24

    Nice question, but I'm not sure we can get a heatmap such as the one depicted in (1).

    ResponderExcluir

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