Communities

Consider the undirected graph shown below. The network contains two dense regions: nodes (1-4) and nodes (5-7), connected through node 3. Node 3 also connects to node 8 through the dashed edge (3,8). We wish to apply the Girvan–Newman divisive community detection algorithm, that is based on the betweenness of nodes. Assume that in the first iteration, the dashed edge (3,8) has the highest betweenness and is therefore removed. After removing the edge (3,8), which of the following statements best describes the next step of the algorithm and its structural implications?

A) Since the graph becomes disconnected after removing (3,8), the algorithm terminates immediately and each connected component is taken as a final community.

B) The algorithm recomputes the betweenness of all remaining edges. Because node 3 still acts as the bridge between the two dense regions (1–4 and 5–7), the edges incident to node 3 are expected to gain higher betweenness, making edges such as (3,5) or (3,7) the next candidates for removal.

C) The algorithm does not recompute betweenness after this removal, recalculation only occurs when a cycle is destroyed. Thus, the next edge removed is the one with the smallest degree, typically (5,6).

D) After removing (3,8), the algorithm immediately identifies two dense communities because it relies on maximizing the internal degree sum (weak-community criterion), not shortest-path structure.

E) None of the above


Original idea by: Thiago Soares Laitz

Comentários

  1. Joao Meidanis15 de novembro de 2025 às 06:33

    Questão interessante, mas me deixa um pouco desconfortável. Como ter certeza de que (3,8) seria a primeira a ser retirada? Não gosto de basear uma questão inteira em premissas dúbias.

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