Question about Communities

A group of network scientists is analyzing a large social network to uncover community structures. They are evaluating several theoretical principles and algorithmic strategies to decide which framework better explains the observed patterns. After reviewing the literature, they make the following statements:

I. A community structure should balance internal density and external sparsity; however, a subgraph that maximizes internal density alone may fail to capture community boundaries consistent with the overall network topology.

II. In hierarchical clustering of networks, bottom-up strategies tend to merge nodes with high topological similarity or shared neighbors, while top-down strategies progressively dismantle inter-community links that maintain global connectivity.

III. The distinction between strong and weak communities reflects whether the internal–external link condition must hold for each vertex individually or only on average for the entire subgraph.

IV. Finding all cliques in a large network usually is computationally impractical, since the maximal clique problem is NP-complete.

Which of the statements above are correct?

A) Only I, II, and III are correct.
B) Only II and III are correct.
C) Only I and II are correct.
D) Only I, III, and IV are correct.
E) None of the above.


Original idea by: Mateus de Padua Vicente

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