Network Robustness

The Galactic Federation maintains an interplanetary communication network connecting N = 1000 colonies through hyperspace routes, forming a scale-free structure. Scientists from the Central Observatory have estimated:

⟨k⟩ = 4,    ⟨k²⟩ = 100

The critical threshold fc — the fraction of nodes removed randomly above which the giant component collapses — is given by:

$$ f_c = 1 - \frac{1}{\frac{\langle k^2 \rangle}{\langle k \rangle} - 1} $$

During a cosmic particle storm, 800 out of 1000 colonies lost communication with the network.

Does the Galactic Federation’s network still maintain a giant component (i.e., is it still connected)?
(Hint: first compute fc, then compare it with the fraction f of lost colonies.)

  1. fc = 0.67 — Communication has collapsed.
  2. fc = 0.67 — Communication is still possible.
  3. fc = 0.96 — The network remains connected.
  4. fc = 0.96 — The network has collapsed.
  5. None of the above

Original idea by: Aline Azevedo

Comments

  1. Joao MeidanisNovember 9, 2025 at 7:24 AM

    Questão fácil, mas boa história para os fãs de coisas espaciais. Fico com ela.

    ReplyDelete

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