Degree Correlations Quiz Question

In simple networks (No multi links), there is a conflict between the scale-free property and degree correlations. This conflict arises because in some scale-free and random networks, with degree correlation, may be predicted more than one link between two sufficiently large hubs (As a simple network does not allow them, we have a conflict between degree correlations and the scale-free property).

Consider the following statements:

I - By comparing the structural cutoff (ks) with the natural cutoff (kmax) we can distinguish between two network regimes (No Structural Cutoff and Structural Disassortativity) 

II - Would be expected multiple links for nodes whose degrees are below a given degree threshold (ks).

III - Is possible to have a scale-free network that is neutral or assortative, if we remove all hubs with degrees larger than ks.

IV - Under the Structural Disassortativity regime, the network would have more links between its hubs than the predicted value.


Chose the option that corresponds to the correct statements:


A. I, II, and IV.

B. I, and III.

C. III, and IV.

D. II, III, and IV.

E. None of the above.


Original idea by: Felipe Crispim da Rocha Salvagnini

Comentários

  1. Joao Meidanis12 de junho de 2022 às 06:15

    Interesting question. I have a few comments: (a) why do you say 'with degree correlations' near the beginning of the question? All networks have some level of degree correlation, as measured by e_ij, k_nn or r; (b) when you say, 'may be predicted more than one link', what kind of prediction is this? Please be more specific and say where this prediction comes from; (c) in III, removing all hubs above a threshold may even modify the scale-free nature of the network; are you taking this into account? (d) prediction again mentioned in IV; is this the same prediction as before? Please clarify, and, in any case, explain a bit more about this prediction.

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